Semiorthogonal decomposition of $\mathrm{D}^b(\mathrm{Bun}_2^L)$

TL;DR

This paper constructs a semiorthogonal decomposition of the derived category of vector bundle moduli spaces on curves, using Borel-Weil-Bott theory and $ heta$-stratification, with blocks related to symmetric powers of the curve.

Contribution

It introduces a novel semiorthogonal decomposition framework for derived categories of moduli spaces of vector bundles on curves.

Findings

Semiorthogonal decomposition with blocks given by symmetric powers of the curve

Application of Borel-Weil-Bott theory to moduli space categories

Use of $ heta$-stratification to analyze derived categories

Abstract

We study the derived category of coherent sheaves on various versions of moduli space of vector bundles on curves by the Borel-Weil-Bott theory for loop groups and $\Theta$-stratification, and construct a semiorthogonal decomposition with blocks given by symmetric powers of the curve.