Hilbert polynomials of moduli spaces of rank 2 vector bundles. II
type: Item
instance of: scholarly article
title: Hilbert polynomials of moduli spaces of rank 2 vector bundles. II
zbMATH Open document ID: 0798.14004
DOI: 10.1016/0040-9383(93)90011-J
author: Aaron Bertram
author: András Szenes
published in: Topology
publication date: 1994-11-03T00:00:00Z
review text: [For part I see \textit{A. Szenes}, ibid. 587-597 (1993; see the preceding review).] Let \({\mathcal M}^ C_ 0\) be the moduli space of semi-stable rank 2 vector bundles with fixed even degree determinant on a curve \(C\), and denote by \(L_ 0\) the generator of \(\text{Pic} {\mathcal M}^ C_ 0\). The authors prove the following formula \[ \dim H^ 0 ({\mathcal M}^ C_ 0, L_ 0^{k-2}) = \sum^{k-1}_{J = +} (k/1 - \cos 2j \pi/k)^{g-1}. \] To prove this formula the authors use the Hecke correspondence between the two moduli spaces \({\mathcal M}^ C_ 0\) and \({\mathcal M}^ C_ 1\) to transfer the calculation from \({\mathcal M}^ C_ 0\) to \({\mathcal M}^ C_ 1\).
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 13D40
zbMATH DE Number: 488117
zbMATH Keywords: Hilbert polynomials
zbMATH Keywords: moduli space of semi-stable rank 2 vector
zbMATH Keywords: Hecke correspondence
reviewed by: Valery K. Vedernikov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 488117