Indecomposability of the bounded derived categories of Brill-Noether varieties

TL;DR

This paper proves that the bounded derived category of coherent sheaves on Brill-Noether varieties for general curves is indecomposable when the degree is at most the genus minus one, revealing a fundamental structural property.

Contribution

It establishes the indecomposability of the derived category for a broad class of Brill-Noether varieties, a new result in algebraic geometry.

Findings

Derived category is indecomposable for d ≤ g-1

Results apply to general smooth projective curves

Advances understanding of categorical structures in algebraic geometry

Abstract

We prove that the bounded derived category of coherent sheaves of the Brill-Noether variety $G^{r}_{d}(C)$ that parametrizing linear series of degree $d$ and dimension $r$ on a general smooth projective curve $C$ is indecomposable when $d\leq g(C)-1$.