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HODGE POLYNOMIALS OF SOME MODULI SPACES OF COHERENT SYSTEMS

CRISTIAN GONZÁLEZ–MARTÍNEZ

DG-Payments and Market Infrastructure, European Central Bank, Neue Mainzer Straβe, 60311 Frankfurt am Main, Germany

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

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https://doi.org/10.1142/S0129167X13500146Cited by:0 (Source: Crossref)

Abstract

When k < n, we study the coherent systems that come from a BGN extension in which the quotient bundle is strictly semistable. In this case we describe a stratification of the moduli space of coherent systems. We also describe the strata as complements of determinantal varieties and we prove that these are irreducible and smooth. These descriptions allow us to compute the Hodge polynomials of this moduli space in some cases. In particular, we give explicit computations for the cases in which (n, d, k) = (3, d, 1) and d is even, obtaining from them the usual Poincaré polynomials.

Dedicated to Peter Newstead in testimony of friendship and gratitude

Keywords:

AMSC: 14H60, 14D20, 14F45

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