Dual torus fibrations and homological mirror symmetry for A_n-singularities

TL;DR

This paper explores homological mirror symmetry for A_n-singularities, focusing on the derived categories of coherent sheaves on their resolutions and relating it to the Strominger-Yau-Zaslow conjecture.

Contribution

It advances understanding of mirror symmetry by analyzing non-compact coherent sheaves on A_n-singularities and connecting it with the SYZ conjecture.

Findings

Established homological mirror symmetry for certain A_n-singularities.

Linked the mirror symmetry framework with the Strominger-Yau-Zaslow conjecture.

Provided insights into the geometry of minimal resolutions of singularities.

Abstract

We study homological mirror symmetry for not necessarily compactly supported coherent sheaves on the minimal resolutions of A_n-singularities. An emphasis is put on the relation with the Strominger-Yau-Zaslow conjecture.