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Stability conditions on
products of curves and Hilbert schemes of surfaces
Chunyi Li, Emanuele Macrì, Alexander Perry, Paolo Stellari and Xiaolei Zhao |
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Geometry & Topology 30 (2026) 3485–3512
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Abstract |
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We prove that stability conditions on the derived category of a product of curves of positive genus are uniquely determined by their central charge and the phase of skyscraper sheaves. As an application, we construct stability conditions on Hilbert schemes of points on certain surfaces, including some K3 surfaces of Kummer type. |
Keywords
Bridgeland stability conditions, products of curves,
hyper-Kähler manifolds
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Mathematical Subject Classification
Primary: 14F08, 14J42, 14J60
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References |
Publication
Received: 7 February 2026
Revised: 17 April 2026
Accepted: 18 May 2026
Published: 12 October 2026
Proposed: Dan Abramovich
Seconded: Mark Gross, Kirsten Wickelgren
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Authors |
| Chunyi Li | |
| Mathematical Institute University of Warwick Coventry United Kingdom |
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| Emanuele Macrì | |
| Laboratoire de Mathématiques
d’Orsay Université Paris-Saclay Orsay France |
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| Alexander Perry | |
| Department of Mathematics University of Michigan Ann Arbor, MI United States |
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| Paolo Stellari | |
| Dipartimento di Matematica
“F. Enriques” Università degli Studi di Milano Milan Italy |
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| Xiaolei Zhao | |
| Department of Mathematics University of California, Santa Barbara Santa Barbara, CA United States |
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| © 2026 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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