Poincaré Polynomial of the Moduli Spaces of Parabolic Bundles

Proceedings Mathematical Sciences

Yogish I Holla¹ 

[1] School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 00 00, India$$

关键词: Cohomology;    parabolic vector bundles;    moduli space;    Betti numbers;    Weil conjectures.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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.

【 授权许可】

Unknown