Triangulated categories of singularities and D-branes in Landau-Ginzburg models

Abstract

In spite of physics terms in the title, this paper is purely mathematical. Its purpose is to introduce triangulated categories related to singularities of algebraic varieties and establish a connection of these categories with D-branes in Landau-Ginzburg models.Comment: 24 pp., LaTeX, Dedicated to the blessed memory of Andrei Nikolaevich Tyurin -- adviser and friend, version 2 (some minor changes), accepted to Trudy Steklov Institut