Tropical Algebraic Geometry [Paperback]

These notes present a polished 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 notes are based on a seminar at the Mathematical Research Center in Oberwolfach in October 2004. The intended audience is graduate, post-graduate, and Ph.D. students as well as established researchers in mathematics.

Based on a seminar at the Mathematical Research Center in Oberwolfach in October 2004, this book contains polished notes of three introductory courses to tropical geometry, which give an introduction to the subject and contain some applications.

This book is based on the lectures given at the Oberwolfach Seminar on Tropical Algebraic Geometry in October 2004. Tropical Geometry ?rst appeared as a subject of its own in 2002, while its roots can be traced back at least to Bergmans work [1] on logarithmic limit sets. Tropical Geometry is now a rapidly developing area of mathematics. It is int- twined with algebraic and symplectic geometry, geometric combinatorics, in- grablesystems, and statistical physics. Tropical Geometry can be viewed as a sort of algebraic geometry with the underlying algebra based on the so-called tropical numbers. The tropicalnumbers (the term tropical comesfrom computer science and commemorates Brazil, in particular a contribution of the Brazilian school to the language recognition problem) are the real numbers enhanced with negative in?nity and equipped with two arithmetic operations called tropical addition and tropical multiplication. The tropical addition is the operation of taking the m- imum. The tropical multiplication is the conventional addition. These operations are commutative, associative and satisfy the distribution law. It turns out that such trol&