English

A computational approach to L\"uroth quartics

Algebraic Geometry 2012-08-08 v1

Abstract

A plane quartic curve is called L\"uroth if it contains the ten vertices of a complete pentalateral. White and Miller constructed in 1909 a covariant quartic 4-fold, associated to any plane quartic. We review their construction and we show how it gives a computational tool to detect if a plane quartic is L\"uroth. As a byproduct, the 28 bitangents of a general plane quartic correspond to 28 singular points of the associated White-Miller quartic 4-fold.

Keywords

Cite

@article{arxiv.1208.1372,
  title  = {A computational approach to L\"uroth quartics},
  author = {Giorgio Ottaviani},
  journal= {arXiv preprint arXiv:1208.1372},
  year   = {2012}
}

Comments

16 pages, one figure, two Macaulay2 files as ancillary files

R2 v1 2026-06-21T21:47:15.633Z