Hyperelliptic Gorenstein curves
type: Item
instance of: scholarly article
title: Hyperelliptic Gorenstein curves
zbMATH Open document ID: 0940.14018
DOI: 10.1016/S0022-4049(97)00124-2
author: Karl-Otto Stöhr
published in: Journal of Pure and Applied Algebra
publication date: 2000-07-11T00:00:00Z
review text: The subject of this paper is the moduli space of pointed singular hyperelliptic curves of genus \(g\geq 2\). It is proved that every such curve can be realized as a curve of degree \(2g+2\) on a rational cone in \({\mathbb P}^{g+2}\), not passing through its vertex, its \(g^1_2\) being cut on the curve by the lines of the cone. Moreover every morphism between two such curves is induced by an automorphism of \({\mathbb P}^{g+2}\) itself, which carries the cone to itself. Using this idea, it is proved that the classes of isomorphism of such curves possessing a two-branched point of singularity degree \(\delta \) form a family of dimension \(2g-2\delta\), while the family of those equipped with an unibranched Weierstrass point has dimension \(2g-2\delta -1\) (the dimension of the family with a non-Weierstrass point has dimension \(2g\)). The result is first proved in any characteristic \(p\neq 2\); the case \(p=2\) is then explicitly described.
reviewed by: Alessandro Gimigliano
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 1308296
zbMATH Keywords: moduli space of pointed singular hyperelliptic curves
MaRDI profile type: Publication
cites work: Higher order differentials and Weierstrass points on Gorenstein curves
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description: scientific article; zbMATH DE number 1308296