1.

Record Nr.

UNINA9910788900203321

Titolo

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

©2013

ISBN

1-4704-0940-2

Descrizione fisica

1 online resource (362 p.)

Collana

Contemporary mathematics, , 1098-3627 ; ; 589 , 0271-4132

Classificazione

14T0514T9951M2012J2014M2532P0514C3005E4514H5232S05

Disciplina

516.3/5

Soggetti

Tropical geometry

Combinatorial analysis

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

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.