Hodge polynomials of the moduli spaces of pairs.

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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.
Atiyah, M. F.; Bott, R.: The Yang-Mills equations over Riemann surfaces. Philos. Trans. Roy.Soc. London Ser. A 308 (1982) 523–615. Bertram, A.: Stable pairs and stable parabolic pairs. J. Algebraic Geom. 3 (1994), no. 4, 703–724. Bradlow, S. B.; Daskalopoulos: Moduli of stable pairs for holomorphic bundles over Riemann surfaces. Int. J. Math. 2 (1991), 477–513. Bradlow, S. B.; Garcıa–Prada, O.: Stable triples,equivariant bundles and dimensional reduction. Math. Ann. 304 (1996), no. 2, 225–252. Bradlow, S. B.; Garcıa–Prada, O.; Gothen, P.B: Moduli spaces of holomorphic triples over compact Riemann surfaces. Math. Ann. 328 (2004), no. 1-2, 299–351. Burillo, J.: El polinomio de Poincare–Hodge de un producto simetrico de variedades kahlerianas compactas. Collect. Math. 41 (1990), no. 1, 59–69. Del Baño, S.: On the motive of moduli spaces of rank two vector bundles over a curve. Compositio Math. 131 (2002),no. 1, 1–30. Deligne, P.: Theorie de Hodge I,II,III. In Proc. I.C.M., vol. 1, 1970, pp. 425–430; in Publ. Math.I.H.E.S. 40 (1971), 5–58; ibid. 44 (1974), 5–77. Durfee, A.H.: Algebraic varieties which are a disjoint union of subvarieties, Lecture Notes in Pure Appl. Math. 105, Marcel Dekker, 1987, pp. 99–102. Danivol, V.I.; Khovanskiı, A.G.: Newton polyhedra and an algorithm for computing Hodge-Deligne numbers, Math. U.S.S.R. Izvestiya 29 (1987), 279–298. Desale, U. V.; Ramanan, S.: Poincare polynomials of the variety of stable bundles. Math. Ann.216 (1975), no. 3, 233–244. Earl, R.; Kirwan, F.: The Hodge numbers of the moduli spaces of vector bundles over a Riemann surface. Q. J. Math. 51 (2000), no. 4, 465–483. Garcıa–Prada, O.: Dimensional reduction of stable bundles, vortices and stable pairs. Internat.J. Math. 5 (1994), no. 1, 1–52. Garcıa–Prada, O.; Gothen, P.B.; Muñoz, V.: Betti numbers of the moduli space of rank 3 parabolic Higgs bundles. Memoirs Amer. Math. Soc. In press. Harder, G.; Narasimhan, M. S.: On the cohomology groups of moduli spaces of vector bundles on curves. Math. Ann. 212 (1974/75), 215–248. Newstead, P.E.: Topological properties of some spaces of stable bundles. Topology 6 (1967)241–262. Newstead, P.E.: Characteristic classes of stable bundles of rank 2 over an algebraic curve. Trans.Amer. Math. Soc. 169 (1972), 337–345. Schmitt, A.: A universal construction for the moduli spaces of decorated vector bundles. Transform.Groups 9 (2004), no. 2, 167–209. Thaddeus, M.: Stable pairs, linear systems and the Verlinde formula. Invent. Math. 117 (1994),no. 2, 317–353.