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.
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}
}