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

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