Some arithmetic properties of order-sequences of algebraic curves
type: Item
instance of: scholarly article
title: Some arithmetic properties of order-sequences of algebraic curves
zbMATH Open document ID: 0776.14010
DOI: 10.1016/0022-4049(93)90142-G
author: Arnaldo Garcia
published in: Journal of Pure and Applied Algebra
publication date: 1993-05-16T00:00:00Z
review text: Let \(L\) be the linear system of hyperplane sections on a smooth projective curve embedded in the projective \(N\)-space. For a divisor \(D\) on the curve \(X\), over an algebraically closed field, let \(e(D,P)\) denote the order of \(D\) at \(P\) on \(X\). One defines the order sequence at \(P\) for \(L\) as the \(N+1\) different orders at \(P\) as \(D\) runs through all the divisors in \(L\). The generic order sequence is called the order sequence of \(L\). The author gives a new proof of the inequalities of the order sequence of \(L\) that was shown by \textit{M. Homma} [``Linear systems on curves with no Weierstrass points'', Bol. Soc. Bras. Mat., Nova Ser. 23, No. 1-2, 93-108 (1992)]. In addition he gives equivalent conditions for when equalities hold and an inequality on order-sequences at Weierstrass points on canonical curves.
Mathematics Subject Classification ID: 14H55
Mathematics Subject Classification ID: 14C20
zbMATH DE Number: 167300
zbMATH Keywords: linear system
zbMATH Keywords: generic order sequence
reviewed by: Aigli Papantonopoulou
MaRDI profile type: Publication
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full work available at URL: 0022-4049(93)90142-g
OpenAlex ID: W2076033357
description: scientific article; zbMATH DE number 167300