English

Plane quartics with at least 8 hyperinflection points

Algebraic Geometry 2013-01-10 v1

Abstract

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 whether or not a smooth plane curve of degree at least 4 is determined by its inflection lines is still open. Over a field of characteristic 0, we show that 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.

Keywords

Cite

@article{arxiv.1301.1865,
  title  = {Plane quartics with at least 8 hyperinflection points},
  author = {Marco Pacini and Damiano Testa},
  journal= {arXiv preprint arXiv:1301.1865},
  year   = {2013}
}
R2 v1 2026-06-21T23:06:39.687Z