03840nam 2200577 450 991082742500332120220901065025.01-4704-0940-2(CKB)3360000000464281(EBL)3113321(SSID)ssj0000893456(PQKBManifestationID)11478647(PQKBTitleCode)TC0000893456(PQKBWorkID)10906105(PQKB)10608989(MiAaPQ)EBC3113321(RPAM)17664677(PPN)197102328(EXLCZ)99336000000046428120140613h20132013 uy 0engur|n|---|||||txtccrAlgebraic 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],editorsProvidence, Rhode Island :American Mathematical Society,2013.©20131 online resource (362 p.)Contemporary mathematics,1098-3627 ;5890271-4132Description based upon print version of record.0-8218-9146-4 Includes bibliographical references.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.Contemporary mathematics (American Mathematical Society).5890271-4132Tropical geometryCongressesCombinatorial analysisCongressesTropical geometryCombinatorial analysis516.3/514T0514T9951M2012J2014M2532P0514C3005E4514H5232S05mscBrugallé Erwan1977-CIEM (Universidad de Cantabria),CIEM Workshop on Tropical GeometryMiAaPQMiAaPQMiAaPQBOOK9910827425003321Algebraic and combinatorial aspects of tropical geometry833085UNINA