Derived category and ACM bundles of moduli space of vector bundles on a curve

TL;DR

This paper demonstrates an embedding of the derived category of a curve into that of its moduli space of vector bundles, generalizes existing semiorthogonal decompositions, and constructs a family of ACM bundles over the moduli space.

Contribution

It introduces a new embedding of derived categories, extends semiorthogonal decompositions, and constructs ACM bundles on the moduli space of vector bundles.

Findings

Derived category of a curve embeds into that of the moduli space

Generalization of semiorthogonal decomposition by Narasimhan and Belmans-Mukhopadhyay

Construction of a one-dimensional family of ACM bundles

Abstract

We show that the derived category of a curve is embedded into the derived category of the moduli space of vector bundles on the curve of coprime rank and degree. We also generalize the semiorthogonal decomposition constructed by Narasimhan and Belmans-Mukhopadhyay. Finally, we produce a one-dimensional family of ACM bundles over the moduli space.