Homological Mirror Symmetry and Simple Elliptic Singularities

TL;DR

This paper constructs a full exceptional collection for certain hypersurface singularities and explores its implications for homological mirror symmetry in the context of simple elliptic singularities.

Contribution

It provides a full exceptional collection in the triangulated category of singularities for Fermat type hypersurface singularities and relates it to homological mirror symmetry.

Findings

Established a full exceptional collection for Fermat type hypersurface singularities.

Connected the exceptional collection to homological mirror symmetry for simple elliptic hypersurfaces.

Enhanced understanding of the categorical structure of singularities in mirror symmetry.

Abstract

We give a full exceptional collection in the triangulated category of singularities in the sense of Orlov for a hypersurface singularity of Fermat type, and discuss its relation with homological mirror symmetry for simple elliptic hypersurface singularities.