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The Hodge–Poincaré polynomial of the moduli spaces of stable vector bundles over an algebraic curve

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Let X be a nonsingular complex projective variety that is acted on by a reductive group G and such that \({X^{ss} \neq X_{(0)}^{s}\neq \emptyset}\). We give formulae for the Hodge–Poincaré series of the quotient \({X_{(0)}^{s}/G}\). We use these computations to obtain the corresponding formulae for the Hodge–Poincaré polynomial of the moduli space of properly stable vector bundles when the rank and the degree are not coprime. We compute explicitly the case in which the rank equals 2 and the degree is even.

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  1. Cristian González–Martínez

    Present address: DG-Payments and Market Infrastructure, European Central Bank, Neue Mainzer Straße, 60311, Frankfurt am Main, Germany

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  1. Department of Mathematics, Tufts University, Bromfield-Pearson Building, 503 Boston Avenue, Medford, MA, 02155, USA

    Cristian González–Martínez

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  1. Cristian González–Martínez
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González–Martínez, C. The Hodge–Poincaré polynomial of the moduli spaces of stable vector bundles over an algebraic curve. manuscripta math. 137, 19–55 (2012). https://doi.org/10.1007/s00229-011-0456-7

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  • DOI: https://doi.org/10.1007/s00229-011-0456-7

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