On Brill-Noether loci over Quot schemes and a Torelli theorem

TL;DR

This paper establishes a non-abelian Torelli theorem for smooth projective curves using derived categories of polarized Quot schemes, introducing Brill-Noether loci and Abel-Jacobi maps in this context.

Contribution

It develops a novel approach by working within derived categories of Quot schemes to prove a Torelli-type result for curves, extending classical methods.

Findings

Proves a non-abelian Torelli theorem for smooth projective curves.

Introduces Brill-Noether loci and Abel-Jacobi maps on Quot schemes.

Connects derived categories with classical curve invariants.

Abstract

We prove a non abelian Torelli type result for smooth projective curves by working in the derived category of some associated polarized Quot schemes and defining Brill-Noether loci and Abel-Jacobi maps on them.