Stability of some vector bundles on Hilbert schemes of points on K3 surfaces

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Fabian Reede
  • Ziyu Zhang

Research Organisations

External Research Organisations

  • ShanghaiTech University
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Details

Original languageEnglish
Pages (from-to)315-341
Number of pages27
JournalMathematische Zeitschrift
Volume301
Issue number1
Early online date3 Dec 2021
Publication statusPublished - May 2022

Abstract

Let \(X\) be a projective K3 surfaces. In two examples where there exists a fine moduli space \(M\) of stable vector bundles on \(X\), isomorphic to a Hilbert scheme of points, we prove that the universal family \(\mathcal{E}\) on \(X\times M\) can be understood as a complete flat family of stable vector bundles on \(M\) parametrized by \(X\), which identifies \(X\) with a smooth connected component of some moduli space of stable sheaves on \(M\).

Keywords

    Hilbert schemes, Moduli spaces, Stable sheaves, Universal families

ASJC Scopus subject areas

Cite this

Stability of some vector bundles on Hilbert schemes of points on K3 surfaces. / Reede, Fabian; Zhang, Ziyu.
In: Mathematische Zeitschrift, Vol. 301, No. 1, 05.2022, p. 315-341.

Research output: Contribution to journal › Article › Research › peer review

Reede F, Zhang Z. Stability of some vector bundles on Hilbert schemes of points on K3 surfaces. Mathematische Zeitschrift. 2022 May;301(1):315-341. Epub 2021 Dec 3. doi: 10.1007/s00209-021-02920-6
Reede, Fabian ; Zhang, Ziyu. / Stability of some vector bundles on Hilbert schemes of points on K3 surfaces. In: Mathematische Zeitschrift. 2022 ; Vol. 301, No. 1. pp. 315-341.
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