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HODGE POLYNOMIALS OF THE MODULI SPACES OF PAIRS

VICENTE MUÑOZ

Departamento de Matemáticas, Consejo Superior de Investigaciones Científicas, Serrano 113 bis, 28006 Madrid, Spain

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DANIEL ORTEGA

Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain

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MARIA-JESÚS VÁZQUEZ-GALLO

Departamento de Ingeniería Civil: Servicios Urbanos, Unidad Docente: Matemáticas, Escuela de Ingeniería de Obras Públicas, Universidad Politécnica de Madrid, Alfonso XII 3 y 5, 28014 Madrid, Spain

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https://doi.org/10.1142/S0129167X07004266Cited by:14 (Source: Crossref)

Abstract

Let X be a smooth projective curve of genus g ≥ 2 over the complex numbers. A holomorphic pair on X is a couple (E, ϕ), where E is a holomorphic bundle over X of rank n and degree d, and ϕ ∈ H⁰(E) is a holomorphic section. In this paper, we determine the Hodge polynomials of the moduli spaces of rank 2 pairs, using the theory of mixed Hodge structures. We also deal with the case in which E has fixed determinant.

Keywords:

AMSC: Primary 14F45, Secondary 14D20, Secondary 14H60

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