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Poincaré polynomial of the moduli spaces of parabolic bundles

Yogish I. Holla
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Abstract

In this paper we use Weil conjectures (Deligne's theorem) to calculate the Betti numbers of the moduli spaces of semi-stable parabolic bundles on a curve. The quasi parabolic analogue of the Siegel formula, together with the method of Harder-Narasimhan filtration gives us a recursive formula for the Poincaré polynomials of the moduli. We solve the recursive formula by the method of Zagier, to give the Poincaré polynomial in a closed form. We also give explicit tables of Betti numbers in small rank, and genera.

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Yogish I. Holla. 1999-02-01. Poincaré polynomial of the moduli spaces of parabolic bundles. https://arxiv.org/abs/math/9902002

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