Indecomposability of the bounded derived categories of Brill-Noether varieties

Abstract

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