Homological Projective Duality via Variation of Geometric Invariant Theory Quotients

TL;DR

This paper introduces a geometric method to construct homological projective duals using variations of GIT quotients, extending to Landau-Ginzburg models and relative duality frameworks.

Contribution

It presents a novel geometric approach to derive homological projective duals from GIT variations, applicable to Veronese embeddings and Landau-Ginzburg models.

Findings

Constructed Lefschetz collections from GIT variations

Derived Landau-Ginzburg homological projective duals

Extended duality framework to relative settings

Abstract

We provide a geometric approach to constructing Lefschetz collections and Landau-Ginzburg Homological Projective Duals from a variation of Geometric Invariant Theory quotients. This approach yields homological projective duals for Veronese embeddings in the setting of Landau Ginzburg models. Our results also extend to a relative Homological Projective Duality framework.