Let $C$ be an irreducible smooth complex projective curve of genus $g\geq 2$ 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.

中文翻译：

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曲线与正则系统对称乘积的半正交分解

令 $C$ 为属 $g\geq 2$ 的不可约光滑复射影曲线，令 $C_d$ 为其 $d$-fold 对称积。在本文中，我们研究了$C_d$ 的派生范畴的半正交分解问题。这需要对 $C_d$ 上的规范系统进行调查，特别是它的基位点。