The nonequivariant coherent-constructible correspondence for toric surfaces

TL;DR

This paper proves a conjecture linking coherent sheaves and constructible sheaves for toric surfaces, using semi-orthogonal decompositions and blow-up techniques.

Contribution

It establishes the nonequivariant coherent-constructible correspondence for toric surfaces, advancing understanding of the relationship between algebraic and symplectic geometry.

Findings

Proved the conjecture for toric surfaces.

Described semi-orthogonal decompositions under blow-up.

Compared constructible side with Orlov's theorem.

Abstract

We prove the nonequivariant coherent-constructible correspondence conjectured by Fang-Liu-Treumann-Zaslow in the case of toric surfaces. Our proof is based on describing a semi-orthogonal decomposition of the constructible side under toric point blow-up and comparing it with Orlov's theorem.