Semi-orthogonal decomposition of symmetric products of curves and canonical system

Abstract

Let $C$ be an irreducible smooth complex projective curve of genus $g\ge 2$ and let $C_d$ be its $d$-fold symmetric product. In this paper, we study the question of semi-orthogonal decompositions of the derived category of $C_d$. This entails investigations of the canonical system on $C_d$, in particular its base locus.