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Algebraic and combinatorial aspects of tropical geometry : CIEM Workshop on Tropical Geometry, December 12-16, 2011, International Center for Mathematical Meetings, Castro Urdiales, Spain / / Erwan Brugallé [and four others],editors
| Algebraic and combinatorial aspects of tropical geometry : CIEM Workshop on Tropical Geometry, December 12-16, 2011, International Center for Mathematical Meetings, Castro Urdiales, Spain / / Erwan Brugallé [and four others],editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (362 p.) |
| Disciplina | 516.3/5 |
| Collana | Contemporary Mathematics |
| Soggetto topico |
Tropical geometry
Combinatorial analysis |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0940-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Dedication""; ""Preface""; ""Intersection multiplicity numbers between tropical hypersurfaces""; ""Introduction""; ""1. Toric hypersurfaces""; ""2. Intersection of toric hypersurfaces""; ""3. Tropical hypersurfaces""; ""4. Intersection of tropical hypersurfaces""; ""5. Intersection multiplicity numbers between tropical hypersurfaces""; ""6. Tropical intersection numbers via volumes of Cayley polytopes""; ""7. Non degenenerate tropical complete intersections""; ""References""; ""On the total curvature of tropical hypersurfaces""; ""1. Introduction""; ""2. Preliminary""
""2.1. Total curvature""""2.2. Tropical hypersurfaces""; ""2.3. Real convergent Puiseux series and tropicalisation""; ""2.4. Real tropical hypersurfaces""; ""3. Total curvature of real and complex amoebas""; ""4. Complex and real total curvature of tropical hypersurfaces""; ""4.1. Complex total curvature""; ""4.2. Total curvature of real tropical hypersurfaces""; ""5. Polyhedral total curvature of a real tropical hypersurface.""; ""5.1. Definition and elementary properties""; ""5.2. Elementary simplex case""; ""5.3. Proof of Proposition 5.8""; ""6. Complement""; ""6.1. Tropical lower bound"" ""Tropically unirational varieties""""1. Tropical Unirationality""; ""Acknowledgements""; ""2. Linear spaces, toric varieties, homogenisation, curves""; ""3. Combining reparameterisations""; ""4. Birational projections""; ""5. Very local reparameterisations""; ""6. Concluding remarks""; ""References""; ""A Guide to Tropicalizations""; ""1. Introduction""; ""2. Analytification""; ""3. Tropicalization""; ""4. Models over the valuation ring and reduction""; ""5. Initial degeneration""; ""6. Affine toric schemes over a valuation ring""; ""7. Toric schemes over a valuation ring"" ""6. The layered categories and the corresponding tropicalization functors"" |
| Record Nr. | UNINA-9910480091803321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Algebraic and combinatorial aspects of tropical geometry : CIEM Workshop on Tropical Geometry, December 12-16, 2011, International Center for Mathematical Meetings, Castro Urdiales, Spain / / Erwan Brugallé [and four others],editors
| Algebraic and combinatorial aspects of tropical geometry : CIEM Workshop on Tropical Geometry, December 12-16, 2011, International Center for Mathematical Meetings, Castro Urdiales, Spain / / Erwan Brugallé [and four others],editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (362 p.) |
| Disciplina | 516.3/5 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Tropical geometry
Combinatorial analysis |
| ISBN | 1-4704-0940-2 |
| Classificazione | 14T0514T9951M2012J2014M2532P0514C3005E4514H5232S05 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Dedication -- Preface -- Intersection multiplicity numbers between tropical hypersurfaces -- Introduction -- 1. Toric hypersurfaces -- 2. Intersection of toric hypersurfaces -- 3. Tropical hypersurfaces -- 4. Intersection of tropical hypersurfaces -- 5. Intersection multiplicity numbers between tropical hypersurfaces -- 6. Tropical intersection numbers via volumes of Cayley polytopes -- 7. Non degenerate tropical complete intersections -- References -- On the total curvature of tropical hypersurfaces -- 1. Introduction -- 2. Preliminary -- 2.1. Total curvature -- 2.2. Tropical hypersurfaces -- 2.3. Real convergent Puiseux series and tropicalisation -- 2.4. Real tropical hypersurfaces -- 3. Total curvature of real and complex amoebas -- 4. Complex and real total curvature of tropical hypersurfaces -- 4.1. Complex total curvature -- 4.2. Total curvature of real tropical hypersurfaces -- 5. Polyhedral total curvature of a real tropical hypersurface. -- 5.1. Definition and elementary properties -- 5.2. Elementary simplex case -- 5.3. Proof of Proposition 5.8 -- 6. Complement -- 6.1. Tropical lower bound -- Tropically unirational varieties -- 1. Tropical Unirationality -- Acknowledgements -- 2. Linear spaces, toric varieties, homogenisation, curves -- 3. Combining reparameterisations -- 4. Birational projections -- 5. Very local reparameterisations -- 6. Concluding remarks -- References -- A Guide to Tropicalizations -- 1. Introduction -- 2. Analytification -- 3. Tropicalization -- 4. Models over the valuation ring and reduction -- 5. Initial degeneration -- 6. Affine toric schemes over a valuation ring -- 7. Toric schemes over a valuation ring -- 6. The layered categories and the corresponding tropicalization functors. |
| Record Nr. | UNINA-9910788900203321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Algebraic and combinatorial aspects of tropical geometry : CIEM Workshop on Tropical Geometry, December 12-16, 2011, International Center for Mathematical Meetings, Castro Urdiales, Spain / / Erwan Brugallé [and four others],editors
| Algebraic and combinatorial aspects of tropical geometry : CIEM Workshop on Tropical Geometry, December 12-16, 2011, International Center for Mathematical Meetings, Castro Urdiales, Spain / / Erwan Brugallé [and four others],editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2013 |
| Descrizione fisica | 1 online resource (362 p.) |
| Disciplina | 516.3/5 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Tropical geometry
Combinatorial analysis |
| ISBN | 1-4704-0940-2 |
| Classificazione | 14T0514T9951M2012J2014M2532P0514C3005E4514H5232S05 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Dedication -- Preface -- Intersection multiplicity numbers between tropical hypersurfaces -- Introduction -- 1. Toric hypersurfaces -- 2. Intersection of toric hypersurfaces -- 3. Tropical hypersurfaces -- 4. Intersection of tropical hypersurfaces -- 5. Intersection multiplicity numbers between tropical hypersurfaces -- 6. Tropical intersection numbers via volumes of Cayley polytopes -- 7. Non degenerate tropical complete intersections -- References -- On the total curvature of tropical hypersurfaces -- 1. Introduction -- 2. Preliminary -- 2.1. Total curvature -- 2.2. Tropical hypersurfaces -- 2.3. Real convergent Puiseux series and tropicalisation -- 2.4. Real tropical hypersurfaces -- 3. Total curvature of real and complex amoebas -- 4. Complex and real total curvature of tropical hypersurfaces -- 4.1. Complex total curvature -- 4.2. Total curvature of real tropical hypersurfaces -- 5. Polyhedral total curvature of a real tropical hypersurface. -- 5.1. Definition and elementary properties -- 5.2. Elementary simplex case -- 5.3. Proof of Proposition 5.8 -- 6. Complement -- 6.1. Tropical lower bound -- Tropically unirational varieties -- 1. Tropical Unirationality -- Acknowledgements -- 2. Linear spaces, toric varieties, homogenisation, curves -- 3. Combining reparameterisations -- 4. Birational projections -- 5. Very local reparameterisations -- 6. Concluding remarks -- References -- A Guide to Tropicalizations -- 1. Introduction -- 2. Analytification -- 3. Tropicalization -- 4. Models over the valuation ring and reduction -- 5. Initial degeneration -- 6. Affine toric schemes over a valuation ring -- 7. Toric schemes over a valuation ring -- 6. The layered categories and the corresponding tropicalization functors. |
| Record Nr. | UNINA-9910827425003321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Dynamical scale transform in tropical geometry / / Tsuyoshi Kato (Kyoto University, Japan)
| Dynamical scale transform in tropical geometry / / Tsuyoshi Kato (Kyoto University, Japan) |
| Autore | Kato Tsuyoshi <1961-> |
| Pubbl/distr/stampa | New Jersey : , : World Scientific, , [2017] |
| Descrizione fisica | 1 online resource (270 pages) |
| Disciplina | 516.3/5 |
| Soggetto topico |
Tropical geometry
Geometry, Algebraic |
| ISBN | 981-4635-37-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910149709403321 |
Kato Tsuyoshi <1961->
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| New Jersey : , : World Scientific, , [2017] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Effective Faithful Tropicalizations Associated to Linear Systems on Curves
| Effective Faithful Tropicalizations Associated to Linear Systems on Curves |
| Autore | Kawaguchi Shu |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 2021 |
| Descrizione fisica | 1 online resource (122 pages) |
| Disciplina | 516.3/52 |
| Altri autori (Persone) | YamakiKazuhiko |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Geometry, Algebraic
Tropical geometry Algebraic geometry -- Tropical geometry -- Tropical geometry Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Rigid analytic geometry Algebraic geometry -- Cycles and subschemes -- Divisors, linear systems, invertible sheaves |
| ISBN |
9781470465346
1470465345 |
| Classificazione | 14T0514G2214C20 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title page -- Chapter 1. Introduction -- Notation and Conventions -- Chapter 2. Preliminaries -- 2.1. Semistable models and semistable pairs -- 2.2. Berkovich spaces -- 2.3. Skeleta associated to strictly semistable models -- 2.4. Skeleta associated to strictly semistable pairs -- 2.5. Some properties of skeleta -- 2.6. Tropical geometry -- 2.7. Faithful tropicalization -- Chapter 3. Good models -- 3.1. Good models of -- 3.2. Theory of divisors on Λ-metric graphs -- 3.3. Weighted Λ-metric graphs -- 3.4. Skeleton as a weighted Λ-metric graph (with a finite graph structure) -- 3.5. Construction of a model of ( , ) -- Chapter 4. Unimodular tropicalization of minimal skeleta for ≥2 -- 4.1. Useful lemmas -- 4.2. Fundamental vertical divisors -- 4.3. Stepwise vertical divisors -- 4.4. Edge-base sections and edge-unimodularity sections -- 4.5. Unimodular tropicalization -- Chapter 5. Faithful tropicalization of minimal skeleta for ≥2 -- Notation and terminology of Chapter 5 -- 5.1. Separating points on an edge of connected type -- 5.2. Separating points in different edges -- 5.3. Separating vertices -- 5.4. Faithful tropicalization of the minimal skeleton -- Chapter 6. Faithful tropicalization of minimal skeleta in low genera -- 6.1. Genus 0 case -- 6.2. Genus 1 case -- Chapter 7. Faithful tropicalization of arbitrary skeleta -- Notation and terminology of Chapter 7 -- 7.1. Geodesic paths -- 7.2. Stepwise vertical divisor associated to a point in ( ) -- 7.3. Base sections and -unimodularity sections -- 7.4. Good model -- 7.5. Proof of Proposition 7.8 -- 7.6. Proof of Theorem 1.2 -- 7.7. Upper bound for the dimension of the target space -- Chapter 8. Complementary results -- 8.1. Theorem 1.2 is optimal for curves in low genera -- 8.2. A very ample line bundle that does not admit a faithful tropicalization -- 8.3. Comparison with [42].
Chapter 9. Limit of tropicalizations by polynomials of a bounded degree -- 9.1. Statement of the result -- 9.2. Polynomial of bounded degree that separates two points -- 9.3. Proof of Theorem 1.7 -- Bibliography -- Subject Index -- Symbol Index -- Back Cover. |
| Record Nr. | UNINA-9910970819103321 |
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Kawaguchi Shu
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| Providence : , : American Mathematical Society, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mirror symmetry and tropical geometry : NSF-CBMS Conference on Tropical Geometry and Mirror Symmetry, December 13-17, 2008, Kansas State University, Manhattan, Kansas / / Ricardo Castaño-Bernard, Yan Soibelman, Ilia Zharkov, editors
| Mirror symmetry and tropical geometry : NSF-CBMS Conference on Tropical Geometry and Mirror Symmetry, December 13-17, 2008, Kansas State University, Manhattan, Kansas / / Ricardo Castaño-Bernard, Yan Soibelman, Ilia Zharkov, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2010] |
| Descrizione fisica | 1 online resource (184 p.) |
| Disciplina | 516.3/5 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Tropical geometry
Calabi-Yau manifolds Algebraic varieties Symmetry (Mathematics) Mirror symmetry |
| Soggetto genere / forma | Electronic books. |
| ISBN |
0-8218-8206-6
0-8218-5851-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""References""""Motivic Donaldson-Thomas invariants: summary of results""; ""On the structure of supersymmetric T3 fibrations""; ""Log Hodge groups on a toric Calabi-Yau degeneration""; ""Tropical theta characteristics"" |
| Record Nr. | UNINA-9910480582903321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2010] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mirror symmetry and tropical geometry : NSF-CBMS Conference on Tropical Geometry and Mirror Symmetry, December 13-17, 2008, Kansas State University, Manhattan, Kansas / / Ricardo Castaño-Bernard, Yan Soibelman, Ilia Zharkov, editors
| Mirror symmetry and tropical geometry : NSF-CBMS Conference on Tropical Geometry and Mirror Symmetry, December 13-17, 2008, Kansas State University, Manhattan, Kansas / / Ricardo Castaño-Bernard, Yan Soibelman, Ilia Zharkov, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2010] |
| Descrizione fisica | 1 online resource (184 p.) |
| Disciplina | 516.3/5 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Tropical geometry
Calabi-Yau manifolds Algebraic varieties Symmetry (Mathematics) Mirror symmetry |
| ISBN |
0-8218-8206-6
0-8218-5851-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Closed form expressions for Hodge numbers of complete intersection Cabali-Yau threefolds in toric varieties / Charles F. Doran and Andrey Y. Novoseltsev -- Anchored Lagrangian submanifolds and their Floer theory / Kenji Fukaya [and others] -- Motivic Donaldson-Thomas invariants : summary of results / Maxim Kontsevich and Yan Soibelman -- On the structure of supersymmetric T³ fibrations / David R. Morison -- Log Hodge groups on a toric Calabi-Yau degeneration / Helge Ruddat -- Tropical theta characteristics / Ilia Zharkov. |
| Record Nr. | UNINA-9910788633403321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2010] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mirror symmetry and tropical geometry : NSF-CBMS Conference on Tropical Geometry and Mirror Symmetry, December 13-17, 2008, Kansas State University, Manhattan, Kansas / / Ricardo Castaño-Bernard, Yan Soibelman, Ilia Zharkov, editors
| Mirror symmetry and tropical geometry : NSF-CBMS Conference on Tropical Geometry and Mirror Symmetry, December 13-17, 2008, Kansas State University, Manhattan, Kansas / / Ricardo Castaño-Bernard, Yan Soibelman, Ilia Zharkov, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2010] |
| Descrizione fisica | 1 online resource (184 p.) |
| Disciplina | 516.3/5 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Tropical geometry
Calabi-Yau manifolds Algebraic varieties Symmetry (Mathematics) Mirror symmetry |
| ISBN |
0-8218-8206-6
0-8218-5851-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Closed form expressions for Hodge numbers of complete intersection Cabali-Yau threefolds in toric varieties / Charles F. Doran and Andrey Y. Novoseltsev -- Anchored Lagrangian submanifolds and their Floer theory / Kenji Fukaya [and others] -- Motivic Donaldson-Thomas invariants : summary of results / Maxim Kontsevich and Yan Soibelman -- On the structure of supersymmetric T³ fibrations / David R. Morison -- Log Hodge groups on a toric Calabi-Yau degeneration / Helge Ruddat -- Tropical theta characteristics / Ilia Zharkov. |
| Record Nr. | UNINA-9910822705003321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2010] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Tropical and idempotent mathematics : International Workshop Tropical-07, Tropical and idempotent mathematics, August 25-30, 2007, Independent University of Moscow and Laboratory J.-V. Poncelet / / G.L. Litvinov, S.N. Sergeev, editors
| Tropical and idempotent mathematics : International Workshop Tropical-07, Tropical and idempotent mathematics, August 25-30, 2007, Independent University of Moscow and Laboratory J.-V. Poncelet / / G.L. Litvinov, S.N. Sergeev, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2009] |
| Descrizione fisica | 1 online resource (394 p.) |
| Disciplina | 516.3/5 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Idempotents
Tropical geometry Mathematical physics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
0-8218-8174-4
0-8218-4782-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Tropical Convex Hull Computations""""Complex Roots of Systems of Tropical Equations and Stability of Electrical Power Networks""; ""Dequantization, Statistical Mechanics and Econophysics""; ""Graph Selectors and the Max-Plus Finite Element Method""; ""Complexity Reduction, Cornices and Pruning""; ""Tropical Analysis of Plurisubharmonic Singularities""; ""Multiorder, Kleene Stars and Cyclic Projectors in the Geometry of Max Cones""; ""A Tropical Version of the Schauder Fixed Point Theorem""; ""Tropical Cones Defined by Max-linear Inequalities""
""Minimum Representing Measures in Idempotent Analysis"" |
| Record Nr. | UNINA-9910481000803321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2009] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Tropical and idempotent mathematics : International Workshop Tropical-07, Tropical and idempotent mathematics, August 25-30, 2007, Independent University of Moscow and Laboratory J.-V. Poncelet / / G.L. Litvinov, S.N. Sergeev, editors
| Tropical and idempotent mathematics : International Workshop Tropical-07, Tropical and idempotent mathematics, August 25-30, 2007, Independent University of Moscow and Laboratory J.-V. Poncelet / / G.L. Litvinov, S.N. Sergeev, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2009] |
| Descrizione fisica | 1 online resource (394 p.) |
| Disciplina | 516.3/5 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Idempotents
Tropical geometry Mathematical physics |
| ISBN |
0-8218-8174-4
0-8218-4782-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Tropical Convex Hull Computations -- Complex Roots of Systems of Tropical Equations and Stability of Electrical Power Networks -- Dequantization, Statistical Mechanics and Econophysics -- Graph Selectors and the Max-Plus Finite Element Method -- Complexity Reduction, Cornices and Pruning -- Tropical Analysis of Plurisubharmonic Singularities -- Multiorder, Kleene Stars and Cyclic Projectors in the Geometry of Max Cones -- A Tropical Version of the Schauder Fixed Point Theorem -- Tropical Cones Defined by Max-linear Inequalities -- Minimum Representing Measures in Idempotent Analysis. |
| Record Nr. | UNINA-9910788798103321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2009] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Soggetto topico
-
Tropical geometry
(21)
- Idempotents (6)
- Geometry, Algebraic (5)
- Mirror symmetry (4)
- Algebraic varieties (3)