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

TL;DR

This paper investigates the semi-orthogonal decomposition of the derived category of symmetric products of smooth projective curves, focusing on the canonical system and its base locus.

Contribution

It provides new insights into the structure of derived categories of symmetric products of curves and analyzes the canonical system's properties.

Findings

Semi-orthogonal decompositions constructed for $C_d$

Analysis of the base locus of the canonical system

New structural results on derived categories of symmetric products

Abstract

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.