Singular locus of the theta divisor for vector bundles of rank two
type: Item
instance of: scholarly article
title: Singular locus of the theta divisor for vector bundles of rank two
zbMATH Open document ID: 0828.14010
DOI: 10.1007/BF02572376
author: Montserrat Teixidor i Bigas
published in: Mathematische Zeitschrift
publication date: 1996-01-08T00:00:00Z
full work available at URL: https://eudml.org/doc/174784
review text: Let \(F\) be a generic vector bundle of rank \(n'\) and degree \(d'\). Denote by \(W^r_{n,d} (F)\) the sets of vector bundles \(E\) of rank \(n\) and degree \(d\) such that \(h^0 (E \otimes F) \geq r + 1\). When \(n = 1\) and \(F\) is a line bundle, these are the classical Brill-Noether loci. From the theory of determinantal varieties, one expects the singular locus to be \(W^{r + 1}_{n,d} (F)\). This is true in the classical case. We show that the result fails for \(n = 2\) and rank \(F = 2\) and we determine exactly the singular locus in this case.
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14M12
Mathematics Subject Classification ID: 14K25
zbMATH DE Number: 795032
zbMATH Keywords: theta divisor
zbMATH Keywords: vector bundle
zbMATH Keywords: Brill-Noether locus
zbMATH Keywords: determinantal varieties
MaRDI profile type: Publication
cites work: Vector Bundles Over an Elliptic Curve
cites work: Q3347989
cites work: Groupe de Picard des variétés de modules de fibrés semi-stable sur les courbes algébriques. (Picard groups of moduli varieties of semi- stable bundles on algebraic curves)
cites work: Q4750778
cites work: A Riemann theorem for the theta divisors on moduli spaces of stable fibre bundles over a curve
cites work: Special divisors and vector bundles
cites work: Brill-Noether theory for stable vector bundles
cites work: Moduli spaces of (semi)stable vector bundles on tree-like curves
cites work: A Riemann Singularity Theorem for Generalised Brill - Noether Loci
OpenAlex ID: W2088147384
description: scientific article; zbMATH DE number 795032