Tropical Algebraic Geometry

Illia Itenberg, Grigory Mikhalkin, Eugenii Shustin (auth.)3764383097, 9783764383091, 9783764383107, 3764383100

Tropical geometry is algebraic geometry over the semifield of tropical numbers, i.e., the real numbers and negative infinity enhanced with the (max,+)-arithmetics. Geometrically, tropical varieties are much simpler than their classical counterparts. Yet they carry information about complex and real varieties.

These notes present an introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject. It consists of three chapters which complete each other and give a possibility for non-specialists to make the first steps in the subject which is not yet well represented in the literature. The intended audience is graduate, post-graduate, and Ph.D. students as well as established researchers in mathematics.

Table of contents :
Front Matter….Pages i-ix
Introduction to tropical geometry….Pages 1-15
Patchworking of algebraic varieties….Pages 17-76
Applications of tropical geometry to enumerative geometry….Pages 77-96
Back Matter….Pages 97-104