03841nam 2200601 450 991048009180332120180731045130.01-4704-0940-2(CKB)3360000000464281(EBL)3113321(SSID)ssj0000893456(PQKBManifestationID)11478647(PQKBTitleCode)TC0000893456(PQKBWorkID)10906105(PQKB)10608989(MiAaPQ)EBC3113321(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 ;Volume 589Description 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 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""Contemporary mathematics (American Mathematical Society) ;Volume 589.Tropical geometryCongressesCombinatorial analysisCongressesElectronic books.Tropical geometryCombinatorial analysis516.3/5Brugallé Erwan1977-CIEM (Universidad de Cantabria),CIEM Workshop on Tropical GeometryMiAaPQMiAaPQMiAaPQBOOK9910480091803321Algebraic and combinatorial aspects of tropical geometry833085UNINA