Stable vector bundles on generalized Kummer varieties

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Fabian Reede
  • Ziyu Zhang

Organisationseinheiten

Externe Organisationen

  • ShanghaiTech University
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)1015-1031
Seitenumfang17
FachzeitschriftForum Mathematicum
Jahrgang34
Ausgabenummer4
Frühes Online-Datum20 Apr. 2022
PublikationsstatusVeröffentlicht - 1 Juli 2022

Abstract

Let \(A\) be an abelian surface. We construct two complete families of stable vector bundles on the generalized Kummer variety \(K_n(A)\). The first is the family of tautological bundles associated to stable bundles on \(A\), and the second is the family of the ''wrong-way'' fibers of a universal family of stable bundles on the dual abelian variety \(\widehat{A}\) parametrized by \(K_n(A)\). Each family exhibits a smooth connected component in the moduli space of stable bundles on \(K_n(A)\).

ASJC Scopus Sachgebiete

Zitieren

Stable vector bundles on generalized Kummer varieties. / Reede, Fabian; Zhang, Ziyu.
in: Forum Mathematicum, Jahrgang 34, Nr. 4, 01.07.2022, S. 1015-1031.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Reede F, Zhang Z. Stable vector bundles on generalized Kummer varieties. Forum Mathematicum. 2022 Jul 1;34(4):1015-1031. Epub 2022 Apr 20. doi: 10.1515/forum-2021-0249
Reede, Fabian ; Zhang, Ziyu. / Stable vector bundles on generalized Kummer varieties. in: Forum Mathematicum. 2022 ; Jahrgang 34, Nr. 4. S. 1015-1031.
Download
@article{47f152b7be894c3d87b669f631ad88a6,
title = "Stable vector bundles on generalized Kummer varieties",
abstract = "Let \(A\) be an abelian surface. We construct two complete families of stable vector bundles on the generalized Kummer variety \(K_n(A)\). The first is the family of tautological bundles associated to stable bundles on \(A\), and the second is the family of the ''wrong-way'' fibers of a universal family of stable bundles on the dual abelian variety \(\widehat{A}\) parametrized by \(K_n(A)\). Each family exhibits a smooth connected component in the moduli space of stable bundles on \(K_n(A)\)",
keywords = "generalized Kummer varieties, moduli spaces, Stable sheaves",
author = "Fabian Reede and Ziyu Zhang",
note = "Acknowledgments: We thank the referee for carefully reading a previous version of the manuscript and several suggestions for improvement.",
year = "2022",
month = jul,
day = "1",
doi = "10.1515/forum-2021-0249",
language = "English",
volume = "34",
pages = "1015--1031",
journal = "Forum Mathematicum",
issn = "0933-7741",
publisher = "Walter de Gruyter GmbH",
number = "4",

}

Download

TY - JOUR

T1 - Stable vector bundles on generalized Kummer varieties

AU - Reede, Fabian

AU - Zhang, Ziyu

N1 - Acknowledgments: We thank the referee for carefully reading a previous version of the manuscript and several suggestions for improvement.

PY - 2022/7/1

Y1 - 2022/7/1

N2 - Let \(A\) be an abelian surface. We construct two complete families of stable vector bundles on the generalized Kummer variety \(K_n(A)\). The first is the family of tautological bundles associated to stable bundles on \(A\), and the second is the family of the ''wrong-way'' fibers of a universal family of stable bundles on the dual abelian variety \(\widehat{A}\) parametrized by \(K_n(A)\). Each family exhibits a smooth connected component in the moduli space of stable bundles on \(K_n(A)\)

AB - Let \(A\) be an abelian surface. We construct two complete families of stable vector bundles on the generalized Kummer variety \(K_n(A)\). The first is the family of tautological bundles associated to stable bundles on \(A\), and the second is the family of the ''wrong-way'' fibers of a universal family of stable bundles on the dual abelian variety \(\widehat{A}\) parametrized by \(K_n(A)\). Each family exhibits a smooth connected component in the moduli space of stable bundles on \(K_n(A)\)

KW - generalized Kummer varieties

KW - moduli spaces

KW - Stable sheaves

UR - http://www.scopus.com/inward/record.url?scp=85129244168&partnerID=8YFLogxK

U2 - 10.1515/forum-2021-0249

DO - 10.1515/forum-2021-0249

M3 - Article

VL - 34

SP - 1015

EP - 1031

JO - Forum Mathematicum

JF - Forum Mathematicum

SN - 0933-7741

IS - 4

ER -