On the Enumerative Geometry of Pascal's Hexagram
Algebraic Geometry
2023-03-21 v1
Abstract
Given six points on a nonsingular conic in the complex projective plane, Pascal's theorem says that the three intersection points are collinear. The line containing them is called a pascal, and we get altogether such lines by permuting the points. In this paper, we consider the enumerative problem of finding the number of sextuples which correspond to three pre-specified pascals. We use computational techniques in commutative algebra to solve this problem in all cases. The results are tabulated using the so-called 'dual' notation for pascals, which is based upon the outer automorphism of .
Cite
@article{arxiv.2303.10319,
title = {On the Enumerative Geometry of Pascal's Hexagram},
author = {Jaydeep Chipalkatti},
journal= {arXiv preprint arXiv:2303.10319},
year = {2023}
}