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Stable vector bundles on generalized Kummer varieties

  • Fabian Reede ORCID logo EMAIL logo and Ziyu Zhang
Published/Copyright: April 20, 2022

Abstract

For an abelian surface A, we explicitly construct two new families of stable vector bundles on the generalized Kummer variety Kn(A) for n2. 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 surface A^ parametrized by Kn(A). Each family exhibits a smooth connected component in the moduli space of stable bundles on Kn(A), which is holomorphic symplectic but not simply connected, contrary to the case of K3 surfaces.


Communicated by Jan Bruinier


Acknowledgements

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

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Received: 2021-09-30
Revised: 2022-02-21
Published Online: 2022-04-20
Published in Print: 2022-07-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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