Variations on Pascal’s theorem

期刊论文
发表日期：

2025年6月9日

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Ciro Ciliberto,
Rick Miranda

摘要

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 $d+4$ $d + 4$ points to lie on rational normal curves. A collection of problems of Pascal type are considered for quadric surfaces in ${\mathbb {P}}^3$ $P^{3}$ . Finally we re-prove, using computer algebra methods, a remarkable theorem of Richmond, Segre, and Brown for quadrics in ${\mathbb {P}}^4$ $P^{4}$ containing five general lines.