Introduction to tropical geometry /

Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear fun...

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Bibliographic Details
Main Author:	Maclagan, Diane, 1974- (Author)
Other Authors:	Sturmfels, Bernd, 1962-
Format:	Book
Language:	English
Published:	Providence, Rhode Island : American Mathematical Society, [2015]
Series:	Graduate studies in mathematics ; v. 161.
Subjects:	Tropical geometry > Study and teaching (Graduate) Geometry, Algebraic > Study and teaching (Graduate) Géométrie tropicale > Étude et enseignement (2e et 3e cycles) Géométrie algébrique > Étude et enseignement (2e et 3e cycles) Tropische Geometrie Algebraic geometry > Tropical geometry > Tropical geometry. Combinatorics > Designs and configurations > Matroids, geometric lattices. Field theory and polynomials > Topological fields > Non-Archimedean valued fields. Commutative algebra > Computational aspects and applications > Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) Algebraic geometry > Special varieties > Toric varieties, Newton polyhedra. Linear and multilinear algebra; matrix theory > Basic linear algebra > Max-plus and related algebras. Convex and discrete geometry > Polytopes and polyhedra > Lattice polytopes (including relations with commutative algebra and algebraic geometry)

Table of Contents:

1. Tropical Islands
2. Building Blocks
3. Tropical Varieties
4. Tropical Rain Forest
5. Tropical Garden
6. Tropic Connections.