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

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

The Gods of My Father Terah’: Abraham the Iconoclast and the Polemics with the Divine Body Traditions in the Apocalypse of Abraham

The first eight chapters of the Apocalypse of Abraham recount the early years of the young hero of the faith who is depicted as a fighter against the idolatrous practices of his father Terah. The conceptual developments found in this section of the work, especially in the depictions of the idolatrous statues, seem to play an important role in the work\u27s overall retraction of the anthropomorphic understanding of the deity. In the depictions of the idol Bar-Eshath (`the Son of Fire\u27) and some other human-like figures, whose features are vividly reminiscent of the familiar attributes of the anthropomorphic portrayals of the deity in Ezekiel and some other biblical and pseudepigraphical accounts, one can detect subtle polemics with the divine body traditions. This article investigates these conceptual developments in the Apocalypse of Abraham and seeks to understand their place in the larger anti-corporeal ideology of the Slavonic pseudepigraphon

Triangulated categories of singularities and equivalences between Landau-Ginzburg models

In this paper we prove an existence of some type of equivalences between triangulated categories of singularities for varieties of different dimensions. This class of equivalences generalizes so called Kn\"orrer periodicity. As consequence we get equivalences between categories of D-branes of type B on Landau-Ginzburg models of different dimensions.Comment: 14 pp., LaTe