Derived categories of curves as components of Fano manifolds

TL;DR

This paper demonstrates that the derived category of a generic curve of genus greater than one can be embedded into the derived category of a related Fano manifold, revealing deep connections between curve geometry and Fano varieties.

Contribution

It establishes a new embedding of the derived category of a generic curve into that of a moduli space of stable bundles, linking curve theory with Fano manifold categories.

Findings

Derived category of a generic curve embeds into that of a Fano manifold.

Shows a new relationship between curve geometry and Fano manifolds.

Provides tools for understanding derived categories of moduli spaces.

Abstract

We prove that the derived category $D(C)$ of a generic curve of genus greater than one embeds into the derived category $D(M)$ of the moduli space $M$ of rank two stable bundles on $C$ with fixed determinant of odd degree.