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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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Abstract

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
References:

D. Arapura and S.-J. Kang, Coniveau and the Grothendieck group of varieties, Michigan Math. J. 54 (2006) 611–622.

M. F. Atiyah and R. Bott, The Yang–Mills equations over Riemann surfaces, Philos. Trans. R. Soc. London Ser. A 308 (1982) 523–615.

A. Bertram, Stable pairs and stable parabolic pairs, J. Algebraic Geom. 3 (1994)703–724.

S. B. Bradlow and G. Daskalopoulos, Moduli of stable pairs for holomorphic bundles over Riemann surfaces, Internat. J. Math. 2 (1991) 477–513.

S. B. Bradlow and O. Garcıa-Prada, Stable triples,equivariant bundles and dimensional reduction,Math. Ann. 304 (1996) 225–252.

S. B. Bradlow, O. Garcıa-Prada and P. B. Gothen, Moduli spaces of holomorphic triples over compact Riemann surfaces, Math. Ann. 328 (2004) 299–351.

P. Deligne, Th´eorie de Hodge I, in Proc. I.C.M., Vol. 1 (1970), pp. 425–430.

P. Deligne, Theorie de Hodge II, in Publ. Math. I.H.E.S. 40 (1971) 5–58.

P. Deligne, Theorie de Hodge III, in Publ. Math. I.H.E.S. 44 (1974) 5–77.

O. Garcıa-Prada, Dimensional reduction of stable bundles, vortices and stable pairs,Internat. J. Math. 5 (1994) 1–52.

I. G. Macdonald, Symmetric products of an algebraic curve, Topology 1 (1962)319–343.

V. Muñoz, Hodge polynomials of the moduli spaces of rank 3 pairs, Geom. Dedicata 136 (2008) 17–46.

V. Muñoz, Torelli theorem for the moduli spaces of pairs, Math. Proc. Cambridge Phil. Soc. 146 (2009) 675–693.Int. J

V. Muñoz, D. Ortega and M.-J. Vazquez-Gallo, Hodge polynomials of the moduli spaces of pairs, Internat. J. Math. 18 (2007) 695–721.

C. A. M. Peters and J. H. M. Steenbrink, Mixed Hodge Structures, A Series of Modern Surveys in Mathematics, Vol. 25 (Springer, 2008).

A. Schmitt, A universal construction for the moduli spaces of decorated vector bundles,Transform. Groups 9 (2004) 167–209.

Deposited On:05 Nov 2012 11:33
Last Modified:07 Feb 2014 09:40

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