Homological mirror symmetry for invertible polynomials in two variables

Abstract

In this paper, we give a proof of homological mirror symmetry for two variable invertible polynomials, where the symmetry group on the $B$-side is taken to be maximal. The proof involves an explicit gluing construction of the Milnor fibres, and as an application, we prove derived equivalences between certain nodal stacky curves, some of whose irreducible components have non-trivial generic stabiliser.

33 Pages, 3 figures. Comments welcome! V4 agrees with published version

References in corpus (5)

• FJRW rings and Landau-Ginzburg Mirror Symmetry
• Arithmetic mirror symmetry for the 2-torus
• Homological Mirror Symmetry and Simple Elliptic Singularities
• Categories of singularities of invertible polynomials
• Fukaya category for Landau-Ginzburg orbifolds

Cited by in corpus (2)

• Homological mirror symmetry for Milnor fibers of simple singularities
• Mirror symmetry for Berglund-Hübsch Milnor fibers