Publication: Hodge polynomials of the moduli spaces of rank 3 pairs
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2008
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Springer
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Let X be a smooth projective curve of genus g >= 2 over the complex numbers. A holomorphic triple (E(1), E(2), phi) on X consists of two holomorphic vector bundles E(1) and E(2) over X and a holomorphic map phi: E(2) -> E(1). There is a concept of stability for triples which depends on a real parameter sigma. In this paper, we determine the Hodge polynomials of the moduli spaces of sigma-stable triples with rk(E(1)) = 3, rk(E(2)) = 1, using the theory of mixed Hodge structures. This gives in particular the Poincare polynomials of these moduli spaces. As a byproduct, we recover the Hodge polynomial of the moduli space of odd degree rank 3 stable vector bundles.
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Bradlow, S.B., García-Prada, O.: Stable triples,quivariant bundles and dimensional reduction. Math.Ann. 304, 225–252 (1996)
Bradlow, S.B., García-Prada, O., Gothen, P.B.: Moduli spaces of holomorphic triples over compact Riemann surfaces. Math. Ann. 328, 299–351 (2004)
Burillo, J.: El polinomio de Poincaré-Hodge de un producto simétrico de variedades kählerianas compactas. Collect. Math. 41, 59–69 (1990)
Del Baño, S.: On the motive of moduli spaces of rank two vector bundles over a curve. Compos.Math. 131, 1–30 (2002)
Deligne, P.: Théorie de Hodge I,II,III. In: Proc. I.C.M., vol. 1, 1970, pp. 425–430; in Publ.Math. I.H.E.S.40, 5–58 (1971); ibid. 44, 5–77 (1974)
Durfee, A.H.: Algebraic varieties which are a disjoint union of subvarieties. Lect. Notes Pure Appl.Math.105, 99–102. Marcel Dekker (1987)
Danivol, V.I., Khovanskiˇı, A.G.: Newton polyhedra and an algorithm for computing Hodge-Deligne numbers. Math. U.S.S.R. Izv. 29, 279–298 (1987)
Earl, R., Kirwan, F.: The Hodge numbers of the moduli spaces of vector bundles over a Riemann surface. Q. J. Math. 51, 465–483 (2000)
García-Prada, O.: Dimensional reduction of stable bundles, vortices and stable pairs. Int. J. Math. 5, 1–52 (1994)
García–Prada, O., Gothen, P.B., Muñoz, V.: Betti numbers of the moduli space of rank 3 parabolic Higgs bundles. Mem. Am. Math. Soc. 187, VIII+80pp (2007)
Muñoz, V., Ortega, D., Vázquez-Gallo, M.-J.: Hodge polynomials of the moduli spaces of pairs. Int. J.Math. 18, 695–721 (2007)
Muñoz, V., Ortega, D., Vázquez-Gallo, M.-J.: Hodge polynomials of the moduli spaces of triples of rank (2, 2). Q. J. Math. (in press). doi:10.1093/qmath/han007
Schmitt, A.: A universal construction for the moduli spaces of decorated vector bundles. Transform.Groups 9, 167–209 (2004)
Thaddeus, M.: Stable pairs, linear systems and the Verlinde formula. Invent. Math. 117, 317–353 (1994)
Zagier, D.: Elementary aspects of the Verlinde formula and of the Harder-Narasimhan-Atiyah-Bott formula.In: Proceedings of the Hirzebruch 65 Conference on Algebraic Geometry (Ramat Gan, 1993).Israel Math. Conf. Proc. 9, 445–462 (1996)