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On the period of Li, Pertusi, and Zhao’s symplectic variety

Part of: Abelian varieties and schemes Families, fibrations Cycles and subschemes

Published online by Cambridge University Press:  04 August 2023

Franco Giovenzana Open the ORCID record for Franco Giovenzana [Opens in a new window] ,
Luca Giovenzana Open the ORCID record for Luca Giovenzana [Opens in a new window]  and
Claudio Onorati Open the ORCID record for Claudio Onorati [Opens in a new window]
Franco Giovenzana
Affiliation:
Fakultät für Mathematik, Technische Universität Chemnitz, Reichenhainer Straße 39, 09126 Chemnitz, Germany e-mail: franco.giovenzana@math.tu-chemnitz.de
Luca Giovenzana
Affiliation:
Mathematical Sciences, Loughborough University, Schofield Building, Epinal Way, Loughborough, Leicestershire LE11 3TU, UK e-mail: L.Giovenzana@lboro.ac.uk Current address: Fakultät für Mathematik, Technische Universität Chemnitz, Reichenhainer Straße 39, 09126 Chemnitz, Germany e-mail: luca.giovenzana@math.tu-chemnitz.de
Claudio Onorati*
Affiliation:
Dipartimento di Matematica, Università di Roma Tor Vergata, via della ricerca scientifica 1, 00133 Rome, Italy
*
e-mail: onorati@mat.uniroma2.it
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Abstract

We extend classical results of Perego and Rapagnetta on moduli spaces of sheaves of type OG10 to moduli spaces of Bridgeland semistable objects on the Kuznetsov component of a cubic fourfold. In particular, we determine the period of this class of varieties and use it to understand when they become birational to moduli spaces of sheaves on a K3 surface.

Keywords

Moduli spaces of Bridgeland semistable objectscubic fourfoldsintermediate Jacobian fibrationsirreducible holomorphic symplectic manifolds

MSC classification

Secondary: 14D20: Algebraic moduli problems, moduli of vector bundles 14K30: Picard schemes, higher Jacobians 14D07: Variation of Hodge structures 14C34: Torelli problem
Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 22
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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Footnotes

F.G. was supported by the DFG through the research grant Le 3093/3-2. L.G. was supported by Engineering and Physical Sciences Research Council (EPSRC) New Investigator Award EP/V005545/1 “Mirror Symmetry for Fibrations and Degenerations.” For the purpose of open access, the author has applied a Creative Commons Attribution (CC BY) license to any Author Accepted Manuscript version arising. C.O. was supported by the PRIN grant CUP E84I19000500006.

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