Jesse Huang, University of Waterloo
Birational coherent constructible correspondence
A major progress towards the Homological Mirror Symmetry (HMS) conjecture of Kontsevich is a version of HMS for toric varieties proved by Fang-Liu-Treumann-Zaslow and Kuwagaki using constructible sheaves, following an approach originally introduced by Bondal. These results suggest that Bondal's approach can be reinvested as a powerful tool to investigate fundamental algebraic questions pertaining to the birational geometry of toric varieties, and have inspired recent works of Hanlon-Hicks-Lazarev and my works with Favero, both used Bondal's map to obtain short resolutions of the diagonal by a specific collection of line bundles. In this talk, I will discuss these results and their connections to noncommutative resolutions of toric singularities and the broader goal to establish birational toric HMS.
MC 5417