Weierstrass loci for vector bundles on curves
type: Item
instance of: scholarly article
title: Weierstrass loci for vector bundles on curves
zbMATH Open document ID: 0852.14009
author: E. Ballico
published in: Illinois Journal of Mathematics
publication date: 1996-12-04T00:00:00Z
review text: Let \(X\) be a smooth complex projective curve, \(E\) a rank \(r\) vector bundle on \(X\) and \(V\subseteq H^0 (X, E)\) a vector space spanning \(E\). \(V\) defines a morphism \(\pi: X\to G(R, n)\), \(n:= \dim (V)\), from \(X\) to a Grassmannian. \textit{D. Perkinson} in his thesis [Trans. Am. Math. Soc. 347, No. 9, 3179-3246 (1995)], introduced the notion of higher order derived bundles and higher order torsion sheaves of \(\pi\) and studied the relations between these notions and the principal part bundles of the pair \((E, V)\). He showed that the ranks of the derived bundles (called ``differential ranks'') give a local normal form of \(\pi\) at a general point of \(X\). In our paper we use his main results to show how often there are examples of \(X\), \(E\) and \(V\) such that the higher order differential ranks are as small as possible, compatibly with the integers \(r\) and \(n\) (e.g. they vanish if \(2r\geq n\)).
Mathematics Subject Classification ID: 14H60
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14H55
Mathematics Subject Classification ID: 30F30
zbMATH DE Number: 926196
zbMATH Keywords: vector bundles on projective curve
zbMATH Keywords: differential ranks
zbMATH Keywords: higher order derived bundles
zbMATH Keywords: higher order torsion sheaves
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 926196