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Hodge structures of the moduli spaces of pairs.


Muñoz, Vicente (2010) Hodge structures of the moduli spaces of pairs. International journal of mathematics, 21 (11). pp. 1505-1529. ISSN 0129-167X

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Let X be a smooth projective curve of genus g >= 2 over C. Fix n >= 2, d epsilon Z. A pair (E, phi) over X consists of an algebraic vector bundle E of rank n and degree d over X and a section phi epsilon H(0)(E). There is a concept of stability for pairs which depends on a real parameter tau. Let M(T) (n, d) be the moduli space of tau-semistable pairs of rank n and degree d over X. Here we prove that the cohomology groups of M(T) (n, d) are Hodge structures isomorphic to direct summands of tensor products of the Hodge structure H(1)(X). This implies a similar result for the moduli spaces of stable vector bundles over X.

Item Type:Article
Uncontrolled Keywords:Moduli space; Complex curve; Holomorphic bundle; Hodge structure.
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:17011

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