Categories of singularities of invertible polynomials

Abstract

We study the categories of singularities coming from Landau-Ginzburg models given by the invertible polynomials. Such categories appear on the B-side of the Berglund-Hübsch mirror symmetry. We provide an efficient method of computing morphism spaces in these categories and explicitly construct full strongly exceptional collections in the cases of small dimensions ($n\le 3$). Finally, we use this construction in order to prove Orlov's conjecture stating that such collections can be chosen to have block decompositions of size one more than the number of variables.

58 pages, 4 tables, 9 figures

References in corpus (3)

• Homological Mirror Symmetry and Simple Elliptic Singularities
• On the homology theory of fibre spaces
• Maximally-graded matrix factorizations for an invertible polynomial of chain type