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E-raamat: Algebraic and Combinatorial Aspects of Tropical Geometry

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  • Formaat: 350 pages
  • Sari: Contemporary Mathematics
  • Ilmumisaeg: 01-Apr-2013
  • Kirjastus: American Mathematical Society
  • ISBN-13: 9781470409401
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  • Formaat: 350 pages
  • Sari: Contemporary Mathematics
  • Ilmumisaeg: 01-Apr-2013
  • Kirjastus: American Mathematical Society
  • ISBN-13: 9781470409401

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This volume contains the proceedings of the CIEM workshop on Tropical Geometry, held December 12-16, 2011, at the International Centre for Mathematical Meetings (CIEM), Castro Urdiales, Spain. Tropical geometry is a new and rapidly developing field of mathematics which has deep connections with various areas of mathematics and physics, such as algebraic geometry, symplectic geometry, complex analysis, dynamical systems, combinatorics, statistical physics, and string theory. As reflected by the content of this volume, this meeting was mainly focused on the geometric side of the tropical world with an emphasis on relations between tropical geometry, algebraic geometry, and combinatorics.

This volume provides an overview of current trends concerning algebraic and combinatorial aspects of tropical geometry through eleven papers combining expository parts and development of modern techniques and tools.
Preface ix
Intersection multiplicity numbers between tropical hypersurfaces
1(20)
Benoit Bertrand
Frederic Bihan
On the total curvature of tropical hypersurfaces
21(24)
Benoit Bertrand
Lucia Lopez De Medrano
Jean-Jacques Risler
Tropical Teichmuller and Siegel spaces
45(42)
Melody Chan
Margarida Melo
Filippo Viviani
Elliptic curves in honeycomb form
87(22)
Melody Chan
Bernd Sturmfels
Tropically unirational varieties
109(16)
Jan Draisma
Bart Frenk
A guide to tropicalizations
125(66)
Walter Gubler
Categorical notions of layered tropical algebra and geometry
191(44)
Zur Izhakian
Manfred Knebusch
Louis Rowen
Tropical realization spaces for polyhedral complexes
235(18)
Eric Katz
Local tropicalization
253(64)
Patrick Popescu-Pampu
Dmitry Stepanov
Some acyclic systems of permutations are not realizable by triangulations of a product of simplices
317(12)
Francisco Santos
Tropical (1, 1)-homology for floor decomposed surfaces
329
Kristin M. Shaw
Erwan Brugallé, Universite Pierre et Marie Curie (Paris 6), France.

Mariá Angélica Cueto, Columbia University, New York, NY, USA, and Goethe-Universitat Frankfurt, Frankfurt am Main, Germany.

Alicia Dickenstein, Universidad de Buenos Aires, Argentina.

Eva-Maria Feichtner, University of Bremen, Germany.

Ilia Itenberg, Universite Pierre et Marie Curie (Paris 6), France.