Non-classical Gorenstein curves of arithmetic genus three and four
type: Item
instance of: scholarly article
title: Non-classical Gorenstein curves of arithmetic genus three and four
zbMATH Open document ID: 0862.14020
DOI: 10.1007/BF02571918
author: Elisabete Sousa Freitas
author: Karl-Otto Stöhr
published in: Mathematische Zeitschrift
publication date: 1995-08-29T00:00:00Z
full work available at URL: https://eudml.org/doc/174743
review text: A complete irreducible non-hyperelliptic Gorenstein curve \(C\) of arithmetic genus \(g\), canonically embedded in the projective space of dimension \(g-1\), is called non-classical, when for each non-singular point \(P\in C\) the osculating hyperplane of \(C\) at \(P\) has contact order larger than \(g-1\). This rather unexpected geometric behaviour can only happen when the characteristic of the constant field is a prime smaller than \(2g-2\). The authors classify the non-classical non-hyperelliptic Gorenstein curves of arithmetic genus three and four; the non-singular case was treated previously by \textit{K. Komiya} [Hiroshima Math. J. 8, 371-400 (1978; Zbl 0406.14007)]. If the arithmetic genus is equal to three, then the classification list consists of one non-singular curve, discovered by F. K. Schmidt, and of five non-classical singular curves. If \(g=4\), then in addition to Komiya's one-parameter family of non-singular curves and an example of F. K. Schmidt the authors obtain various new families of non-classical Gorenstein curves.
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 14G15
zbMATH DE Number: 784084
zbMATH Keywords: prime characteristic
zbMATH Keywords: non-classical non-hyperelliptic Gorenstein curves
zbMATH Keywords: arithmetic genus
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 784084