Poincar\'e polynomial of the moduli spaces of parabolic bundles
Algebraic Geometry
2016-09-07 v1
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 Poincar\'e polynomials of the moduli. We solve the recursive formula by the method of Zagier, to give the Poincar\'e polynomial in a closed form. We also give explicit tables of Betti numbers in small rank, and genera.
Keywords
Cite
@article{arxiv.math/9902002,
title = {Poincar\'e polynomial of the moduli spaces of parabolic bundles},
author = {Yogish I. Holla},
journal= {arXiv preprint arXiv:math/9902002},
year = {2016}
}
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