On the generalized theta divisor
type: Item
instance of: scholarly article
title: On the generalized theta divisor
zbMATH Open document ID: 0890.14018
author: Georg Hein
published in: Beiträge zur Algebra und Geometrie
publication date: 1998-06-25T00:00:00Z
full work available at URL: https://eudml.org/doc/230624
full work available at URL: no.1
review text: Let \(\text{SU}_X(n)\) denote the moduli space of semistable rank \(n\) bundles with trivial determinant on a Riemann surface \(X\) of genus \(>1\). Let \(L\) be the ample generator of the Picard group of \(\text{SU}_X(n)\) [cf. \textit{J.-M. Drezet} and \textit{M. S. Narasimhan}, Invent. Math. 97, No. 1, 53-94 (1989; Zbl 0689.14012)]. The main result of this paper is the base point freeness of the linear system \(|L^{\otimes k}|\), for any integer \(k>(n-1)^2(g-1)\). This was known when \(n=2\) [see \textit{M. Raynaud}, Bull. Soc. Math. Fr. 110, 103-125 (1982; Zbl 0505.14011)] and a weaker bound was found by \textit{J. Le Potier} [Lect. Notes Pure Appl. Math. 179, 83--101 (1996; Zbl 0890.14017)]. This author uses Le Potiers' construction of canonical sections of \(|L^{\otimes k}|\), loc. cit.
Mathematics Subject Classification ID: 14H60
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14K25
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 1018699
zbMATH Keywords: moduli space
zbMATH Keywords: Riemann surface
zbMATH Keywords: base-point free linear system
reviewed by: Emma Previato
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1018699