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Hodge conjecture for the moduli space of semi-stable sheaves over a nodal curve

  • In this article, we prove the Hodge conjecture for a desingularization of the moduli space of rank 2, semi-stable, torsion-free sheaves with fixed odd degree determinant over a very general irreducible nodal curve of genus at least 2. We also compute the algebraic Poincaré polynomial of the associated cohomology ring.

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Author:Ananyo DanORCiDGND, Inder KaurORCiDGND
URN:urn:nbn:de:hebis:30:3-695641
DOI:https://doi.org/10.1007/s10231-022-01225-7
ISSN:1618-1891
Parent Title (Italian):Annali di matematica pura ed applicata
Publisher:Springer
Place of publication:Berlin ; Heidelberg [u.a.]
Document Type:Article
Language:English
Date of Publication (online):2022/05/31
Date of first Publication:2022/05/31
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2023/08/10
Tag:Algebraic Hodge polynomial; Cycle class; Hodge conjecture; Limit mixed Hodge structures; Moduli space of semi-stable sheaves; Nodal curves
Volume:201
Issue:6
Page Number:20
First Page:2907
Last Page:2926
Note:
Open Access funding enabled and organized by Projekt DEAL.
HeBIS-PPN:511656777
Institutes:Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:14-XX ALGEBRAIC GEOMETRY / 14Cxx Cycles and subschemes / 14C30 Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture
14-XX ALGEBRAIC GEOMETRY / 14Dxx Families, fibrations / 14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
14-XX ALGEBRAIC GEOMETRY / 14Dxx Families, fibrations / 14D07 Variation of Hodge structures [See also 32G20]
14-XX ALGEBRAIC GEOMETRY / 14Dxx Families, fibrations / 14D20 Algebraic moduli problems, moduli of vector bundles (For analytic moduli problems, see 32G13)
14-XX ALGEBRAIC GEOMETRY / 14Dxx Families, fibrations / 14D22 Fine and coarse moduli spaces
32-XX SEVERAL COMPLEX VARIABLES AND ANALYTIC SPACES (For infinite-dimensional holomorphy, see 46G20, 58B12) / 32Gxx Deformations of analytic structures / 32G20 Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30]
32-XX SEVERAL COMPLEX VARIABLES AND ANALYTIC SPACES (For infinite-dimensional holomorphy, see 46G20, 58B12) / 32Sxx Singularities [See also 58Kxx] / 32S35 Mixed Hodge theory of singular varieties [See also 14C30, 14D07]
Sammlungen:Universitätspublikationen
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International

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