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Article: Shifted Poisson structures and moduli spaces of complexes
Title | Shifted Poisson structures and moduli spaces of complexes |
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Authors | |
Keywords | Feigin–Odesskii elliptic algebra Moduli space of complexes Quantum projective plane Shifted Poisson structure |
Issue Date | 2018 |
Publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/aim |
Citation | Advances in Mathematics, 2018, v. 338, p. 991-1037 How to Cite? |
Abstract | Shifted Poisson structures and moduli spaces of complexes Zheng Hua, Alexander Polishchuk (Submitted on 29 Jun 2017 (v1), last revised 19 Jul 2017 (this version, v2)) In this paper we study the moduli stack of complexes of vector bundles (with chain isomorphisms) over a smooth projective variety X via derived algebraic geometry. We prove that if X is a Calabi-Yau variety of dimension d then this moduli stack has a (1−d)-shifted Poisson structure. In the case d=1, we construct a natural foliation of the moduli stack by 0-shifted symplectic substacks. We show that our construction recovers various known Poisson structures associated to complex elliptic curves, including the Poisson structure on Hilbert scheme of points on elliptic quantum projective planes studied by Nevins and Stafford, and the Poisson structures on the moduli spaces of stable triples over an elliptic curves considered by one of us. We also relate the latter Poisson structures to the semi-classical limits of the elliptic Sklyanin algebras studied by Feigin and Odesskii. |
Persistent Identifier | http://hdl.handle.net/10722/259344 |
ISSN | 2023 Impact Factor: 1.5 2023 SCImago Journal Rankings: 2.022 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Hua, Z | - |
dc.contributor.author | Polishchuk, A | - |
dc.date.accessioned | 2018-09-03T04:05:39Z | - |
dc.date.available | 2018-09-03T04:05:39Z | - |
dc.date.issued | 2018 | - |
dc.identifier.citation | Advances in Mathematics, 2018, v. 338, p. 991-1037 | - |
dc.identifier.issn | 0001-8708 | - |
dc.identifier.uri | http://hdl.handle.net/10722/259344 | - |
dc.description.abstract | Shifted Poisson structures and moduli spaces of complexes Zheng Hua, Alexander Polishchuk (Submitted on 29 Jun 2017 (v1), last revised 19 Jul 2017 (this version, v2)) In this paper we study the moduli stack of complexes of vector bundles (with chain isomorphisms) over a smooth projective variety X via derived algebraic geometry. We prove that if X is a Calabi-Yau variety of dimension d then this moduli stack has a (1−d)-shifted Poisson structure. In the case d=1, we construct a natural foliation of the moduli stack by 0-shifted symplectic substacks. We show that our construction recovers various known Poisson structures associated to complex elliptic curves, including the Poisson structure on Hilbert scheme of points on elliptic quantum projective planes studied by Nevins and Stafford, and the Poisson structures on the moduli spaces of stable triples over an elliptic curves considered by one of us. We also relate the latter Poisson structures to the semi-classical limits of the elliptic Sklyanin algebras studied by Feigin and Odesskii. | - |
dc.language | eng | - |
dc.publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/aim | - |
dc.relation.ispartof | Advances in Mathematics | - |
dc.subject | Feigin–Odesskii elliptic algebra | - |
dc.subject | Moduli space of complexes | - |
dc.subject | Quantum projective plane | - |
dc.subject | Shifted Poisson structure | - |
dc.title | Shifted Poisson structures and moduli spaces of complexes | - |
dc.type | Article | - |
dc.identifier.email | Hua, Z: huazheng@hku.hk | - |
dc.identifier.authority | Hua, Z=rp01790 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.aim.2018.09.018 | - |
dc.identifier.scopus | eid_2-s2.0-85053807000 | - |
dc.identifier.hkuros | 289657 | - |
dc.identifier.volume | 338 | - |
dc.identifier.spage | 991 | - |
dc.identifier.epage | 1037 | - |
dc.identifier.isi | WOS:000447961200022 | - |
dc.publisher.place | United Kingdom | - |
dc.identifier.issnl | 0001-8708 | - |