Some loci in Teichmüller space for genus seven defined by vanishing thetanulls
type: Item
instance of: scholarly article
title: Some loci in Teichmüller space for genus seven defined by vanishing thetanulls
zbMATH Open document ID: 0815.14019
DOI: 10.1007/BF02567848
author: Robert D. M. Accola
published in: Manuscripta Mathematica
publication date: 1995-07-02T00:00:00Z
full work available at URL: https://eudml.org/doc/155891
review text: The author considers vanishing properties of the theta function for a Riemann surface of genus seven, which are equivalent according to the Riemann vanishing theorem, to the existence on \(W_ 7\) of four complete half-canonical linear series. The following theorem is proved: Suppose \(W_ 7\), Riemann surface of genus 7, admits 4 complete half- canonical linear series \(g^ 1_ 6\), \(h^ 1_ 6\), \(k^ 1_ 6\) and \(l^ 2_ 6\) whose sum is bicanonical. Then one of the following possibilities holds: (i) \(W_ 7\) is hyperelliptic, (ii) \(W_ 7\) is elliptic-hyperelliptic, (iii) \(W_ 7\) is in \({\mathcal N}_ 7\).
Mathematics Subject Classification ID: 14H55
Mathematics Subject Classification ID: 14K25
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 510017
zbMATH Keywords: vanishing of theta function
zbMATH Keywords: Riemann surface of genus seven
zbMATH Keywords: linear series
reviewed by: Victor Enolski
MaRDI profile type: Publication
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OpenAlex ID: W2017651579
description: scientific article; zbMATH DE number 510017