Plane quartics with at least 8 hyperinflection points

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• 作者：Marco Pacini (1)
  Damiano Testa (2)
  
  1. Universidade Federal Fluminense ; Rua M.S. Braga ; Niter贸i ; RJ ; Brazil
  2. Mathematics Institute ; University of Warwick ; Coventry ; CV4 7AL ; UK
  
• 关键词：plane quartics ; inflection line ; hyperinflection line ; Vermeulen鈥檚 list ; 14H50
• 刊名：Bulletin of the Brazilian Mathematical Society
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：45
• 期：4
• 页码：819-836
• 全文大小：169 KB
• 参考文献：1. A. Abreu, M. Pacini and D. Testa. / The general plane quartic is determined by its inflection lines. In preparation.
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  11. D. Lehavi. / Any smooth plane quartic can be reconstructed from its bitangents. Israel J. Math., 146 (2005), 371鈥?79. CrossRef
  12. M. Pacini and D. Testa. / Recovering plane curves of low degree from their inflection lines and inflection points. Israel J. Math., 195(1) (2013), 283鈥?16. CrossRef
  13. A.M. Vermeulen. / Weierstrass points of weight two on curves of genus three. Universiteit van Amsterdam, Amsterdam, 1983. Dissertation, University of Amsterdam, Amsterdam, 1983;With a Dutch summary.
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Mathematical and Computational Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1678-7714

文摘

A recent result shows that a general smooth plane quartic can be recovered from its 24 inflection lines and a single inflection point. Nevertheless, the question of whether or not a smooth plane curve of degree at least 4 is determined fromits inflection lines is still open. Over a field of characteristic 0,we showthat it is possible to reconstruct any smooth plane quartic with at least 8 hyperinflection points by its inflection lines. Our methods apply also in positive characteristic, where we show a similar result, with two exceptions in characteristic 13.