Journal article
Scattering diagrams, stability conditions, and coherent sheaves on ℙ²
- Abstract:
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We show that a purely algebraic structure, a two-dimensional scattering diagram, describes a large part of the wall-crossing behavior of moduli spaces of Bridgeland semistable objects in the derived category of coherent sheaves on P2. This gives a new algorithm computing the Hodge numbers of the intersection cohomology of the classical moduli spaces of Gieseker semistable sheaves on P2, or equivalently the refined Donaldson-Thomas invariants for compactly supported sheaves on local P2.
As applications, we prove that the intersection cohomology of moduli spaces of Gieseker semistable sheaves on P2 is Hodge-Tate, and we give the first non-trivial numerical checks of the general χ-independence conjecture for refined Donaldson-Thomas invariants of one-dimensional sheaves on local P2.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Access Document
- Files:
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-
(Preview, Accepted manuscript, pdf, 764.8KB, Terms of use)
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- Publisher copy:
- 10.1090/jag/795
Authors
- Publisher:
- American Mathematical Society
- Journal:
- Journal of Algebraic Geometry More from this journal
- Volume:
- 31
- Issue:
- 4
- Pages:
- 593-686
- Publication date:
- 2022-06-24
- Acceptance date:
- 2021-09-15
- DOI:
- EISSN:
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1534-7486
- ISSN:
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1056-3911
- Language:
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English
- Keywords:
- Pubs id:
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2301068
- UUID:
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uuid_2f9d4c51-ed5a-43be-9506-30e5aedc3a8e
- Local pid:
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pubs:2301068
- Source identifiers:
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W4283371046
- Deposit date:
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2025-11-03
Terms of use
- Copyright holder:
- University Press, Inc.
- Copyright date:
- 2022
- Rights statement:
- © Copyright 2022 University Press, Inc.
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from American Mathematical Society at https://dx.doi.org/10.1090/jag/795
- Licence:
- Other
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