TY - JOUR

T1 - Stability of some vector bundles on Hilbert schemes of points on K3 surfaces

AU - Reede, Fabian

AU - Zhang, Ziyu

N1 - Funding Information: We thank Nicolas Addington and Andrew Wray for kindly sending us [22 ]. We also thank Norbert Hoffmann for communicating to us Lemma 3.5. We are particularly grateful to the anonymous referee who helped to improve the presentation of the manuscript greatly, and pointed out a mistake in a previous version of Proposition 3.14. In particular, Lemmas 3.12 and 3.13 in the current version are due to the referee. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

PY - 2022/5

Y1 - 2022/5

N2 - 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 \(M\).

AB - 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 \(M\).

KW - Hilbert schemes

KW - Moduli spaces

KW - Stable sheaves

KW - Universal families

UR - http://www.scopus.com/inward/record.url?scp=85120558782&partnerID=8YFLogxK

U2 - 10.1007/s00209-021-02920-6

DO - 10.1007/s00209-021-02920-6

M3 - Article

VL - 301

SP - 315

EP - 341

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

IS - 1

ER -