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Hodge polynomials of the moduli spaces of triples of rank (2,2).

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Muñoz, Vicente and Ortega, Daniel and Vázquez Gallo, M. Jesús (2009) Hodge polynomials of the moduli spaces of triples of rank (2,2). Quarterly Journal of Mathematics , 60 (2). pp. 235-272. ISSN 0033-5606

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Official URL: http://qjmath.oxfordjournals.org/content/60/2/235




Abstract

Let X be a smooth projective curve of genus g ≥ 2 over the complex numbers. A holomorphic triple (E1, E2, φ) on X consists of two holomorphic vector bundles E1 and E2 over X
and a holomorphic map φ: E2 → E1. There is a concept of stability for triples which depends on a real parameter σ. In this paper, we determine the Hodge polynomials of the moduli spaces of σ-stable triples with rk(E1) = rk(E2) = 2, using the theory of mixed Hodge structures (in the cases
that they are smooth and compact). This gives in particular the Poincar´e 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.


Item Type:Article
Uncontrolled Keywords:Moduli space; Complex curve; Stable triple; Hodge polynomial.
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:20887
Deposited On:17 Apr 2013 13:02
Last Modified:12 Dec 2018 15:13

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