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HODGE STRUCTURES OF THE MODULI SPACES OF PAIRS

VICENTE MUÑOZ

Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza Ciencias 3, 28040 Madrid, Spain

https://doi.org/10.1142/S0129167X10006604Cited by:3 (Source: Crossref)

Abstract

Let X be a smooth projective curve of genus g ≥ 2 over ℂ. Fix n ≥ 2, d ∈ ℤ. A pair (E, ϕ) over X consists of an algebraic vector bundle E of rank n and degree d over X and a section ϕ ∈ H⁰(E). There is a concept of stability for pairs which depends on a real parameter τ. Let be the moduli space of τ-semistable pairs of rank n and degree d over X. Here we prove that the cohomology groups of are Hodge structures isomorphic to direct summands of tensor products of the Hodge structure H¹(X). This implies a similar result for the moduli spaces of stable vector bundles over X.

Keywords:

AMSC: 14D20, 14H60, 14F45

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