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

• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , 2013; ©2013
• Descrizione fisica: 1 online resource (362 p.)
• Disciplina: 516.3/5
• Soggetto topico: Tropical geometry; Combinatorial analysis
• Classificazione: 14T0514T9951M2012J2014M2532P0514C3005E4514H5232S05
• Persona (resp. second.): BrugalléErwan <1977->
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• 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.
• Titolo autorizzato: Algebraic and combinatorial aspects of tropical geometry
• ISBN: 1-4704-0940-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910788900203321
• Lo trovi qui: Univ. Federico II
• Serie: Contemporary mathematics (American Mathematical Society). ; 589 . 0271-4132