Atomic objects on hyper-Kähler manifolds

Beckmann, Thorsten

doi:10.1090/jag/830

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Atomic objects on hyper-Kähler manifolds

Author: Thorsten Beckmann
Journal: J. Algebraic Geom.
DOI: https://doi.org/10.1090/jag/830
Published electronically: April 19, 2024
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Abstract: We introduce and study the notion of atomic sheaves and complexes on higher-dimensional hyper-Kähler manifolds and show that they share many of the intriguing properties of simple sheaves on K3 surfaces. For example, we prove formality of the dg algebra of derived endomorphisms for stable atomic bundles. We further demonstrate the characteristics of atomic objects by studying atomic Lagrangian submanifolds. In the appendix, we prove nonexistence results for spherical objects on hyper-Kähler manifolds.

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Additional Information

Thorsten Beckmann
Affiliation: Max–Planck–Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
MR Author ID: 1395781
Email: beckmann@math.uni-bonn.de

Received by editor(s): August 2, 2022
Received by editor(s) in revised form: November 6, 2023, and December 6, 2023
Published electronically: April 19, 2024
Additional Notes: The author was supported by the International Max–Planck Research School on Moduli Spaces of the Max–Planck Society.
Article copyright: © Copyright 2024 University Press, Inc.

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