HODGE POLYNOMIALS OF THE MODULI SPACES OF TRIPLES OF RANK (2, 2)

Authors: Muoz, Vicente; Ortega, Daniel; Vzquez-Gallo, Maria-Jess

Source: Quarterly Journal of Mathematics, Volume 60, Number 2, 5 June 2009 , pp. 235-272(38)

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Abstract:

Let X be a smooth projective curve of genus g 2 over the complex numbers. A holomorphic triple (E₁, E₂, ) on X consists of two holomorphic vector bundles E₁ and E₂ over X and a holomorphic map :E₂ E₁. There is a concept of stability for triples which depends on a real parameter . In this paper, we determine the Hodge polynomials of the moduli spaces of -stable triples with rk(E₁) rk(E₂) 2, using the theory of mixed Hodge structures (in the cases that these moduli spaces are smooth and compact). This gives in particular the Poincar polynomials of these moduli spaces. As a byproduct, we also give the Hodge polynomial of the moduli space of even degree rank 2 stable vector bundles.

Document Type: Research article

DOI: http://dx.doi.org/10.1093/qmath/han007

Publication date: 2009-06-05

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The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. Areas such as algebra, differential geometry, and global analysis receive particular emphasis. However the journal avoids specialization.