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Let X be a smooth projective curve of genus \(g \geq 2\) and M be the moduli space of rank 2 stable vector bundles on X whose determinants are isomorphic to a fixed odd degree line bundle \(L.\) There has been a lot of works studying the moduli, and recently, the bounded derived category of coherent sheaves on M draws lots of attentions. It was proved that the derived category of X can be embedded into the derived category of M (cf. Fonarev and Kuznetsov (J London Math Soc (2) 97:24–46, 2018); Narasimhan (J Geom Phys 122:53–58, 2017; Narasimhan, M. S. (2018). Derived categories of moduli spaces of vector bundles on curves II. In: Geometry, Algebra, Number Theory, and Their Information Technology Applications, pp. 375–382. Springer Proceedings in Mathematics & Statistics, vol. 251. Springer)). In this chapter, we prove that the derived category of the second symmetric product of X can be embedded into derived category of M when X is non-hyperelliptic and \(g \geq 16.\)

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Symmetric Products and Moduli Spaces of Vector Bundles of Curves

  • 章节

  • 发表日期：

    2026年

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  • Kyoung-Seog Lee,
  • M. S. Narasimhan

摘要

Let X be a smooth projective curve of genus \(g \geq 2\) and M be the moduli space of rank 2 stable vector bundles on X whose determinants are isomorphic to a fixed odd degree line bundle \(L.\) There has been a lot of works studying the moduli, and recently, the bounded derived category of coherent sheaves on M draws lots of attentions. It was proved that the derived category of X can be embedded into the derived category of M (cf. Fonarev and Kuznetsov (J London Math Soc (2) 97:24–46, 2018); Narasimhan (J Geom Phys 122:53–58, 2017; Narasimhan, M. S. (2018). Derived categories of moduli spaces of vector bundles on curves II. In: Geometry, Algebra, Number Theory, and Their Information Technology Applications, pp. 375–382. Springer Proceedings in Mathematics & Statistics, vol. 251. Springer)). In this chapter, we prove that the derived category of the second symmetric product of X can be embedded into derived category of M when X is non-hyperelliptic and \(g \geq 16.\)