The Betti numbers of the moduli space of stable sheaves of rank 2 on a ruled surface
type: Item
instance of: scholarly article
title: The Betti numbers of the moduli space of stable sheaves of rank 2 on a ruled surface
zbMATH Open document ID: 0828.14006
DOI: 10.1007/BF01444506
author: Kōta Yoshioka
published in: Mathematische Annalen
publication date: 1996-01-08T00:00:00Z
full work available at URL: https://eudml.org/doc/165342
review text: We shall compute the Betti numbers of moduli spaces of stable sheaves of rank 2 on a ruled surface or \(\mathbb{P}^2\), under some conditions on polarizations and Chern classes. Our approach is the same as that of Harder and Narasimhan. That is, we shall consider the weighted numbers \(\sum_E {1 \over \# \Aut (E)}\) of torsion free sheaves defined over a finite field \(\mathbb{F}_q\) and by using Harder-Narasimhan filtration, we can compute the number of \(\mathbb{F}_q\)-rational points of moduli spaces. Then, by virtue of the Weil conjectures, we obtain the Betti numbers.
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14F45
Mathematics Subject Classification ID: 14J10
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 799558
zbMATH Keywords: number of rational points
zbMATH Keywords: Betti numbers of moduli spaces
zbMATH Keywords: sheaves of rank 2
zbMATH Keywords: Harder-Narasimhan filtration
MaRDI profile type: Publication
cites work: The Yang-Mills equations over Riemann surfaces
cites work: Stable 2-bundles on Hirzebruch surfaces
cites work: La conjecture de Weil. I
cites work: Poincaré polynomials of the variety of stable bundles
cites work: Q4694663
cites work: On the moduli of vector bundles on an algebraic surface
cites work: The Betti numbers of the Hilbert scheme of points on a smooth projective surface
cites work: Perverse sheaves and the cohomology of Hilbert schemes of smooth algebraic surfaces
cites work: Q3960939
cites work: On the cohomology groups of moduli spaces of vector bundles on curves
cites work: Q3346437
cites work: Partial desingularisations of quotients of nonsingular varieties and their Betti numbers
cites work: On the Homology of Compactifications of Moduli Spaces of Vector Bundles Over a Riemann Surface
cites work: Valuative criteria for families of vector bundles on algebraic varieties
cites work: Moduli of stable sheaves. I
cites work: Moduli of stable sheaves. II
cites work: Q3663428
cites work: The Betti numbers of the moduli space of stable sheaves of rank2 on P2.
OpenAlex ID: W53292203
description: scientific article; zbMATH DE number 799558