English

Variations on Pascal's Theorem

Algebraic Geometry 2024-11-13 v1

Abstract

In this paper we present a variety of statements that are in the spirit of the famous theorem of Pascal, often referred to as the Mystic Hexagon. We give explicit equations describing the conditions for d+4d+4 points to lie on rational normal curves. A collection of problems of Pascal type are considered for quadric surfaces in \bbP3\bbP^3. Finally we reprove, using computer algebra methods, a remarkable theorem of Richmond, Segre, and Brown, for quadrics in \bbP4\bbP^4 containing five general lines.

Keywords

Cite

@article{arxiv.2411.07638,
  title  = {Variations on Pascal's Theorem},
  author = {Ciro Ciliberto and Rick Miranda},
  journal= {arXiv preprint arXiv:2411.07638},
  year   = {2024}
}
R2 v1 2026-06-28T19:56:45.520Z