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arXiv · 2411.07638

Variations on Pascal's Theorem

Ciro Ciliberto·Rick Miranda
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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 $d+4$ points to lie on rational normal curves. A collection of problems of Pascal type are considered for quadric surfaces in $\bbP^3$. Finally we reprove, using computer algebra methods, a remarkable theorem of Richmond, Segre, and Brown, for quadrics in $\bbP^4$ containing five general lines.

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Ciro Ciliberto, Rick Miranda. 2024-11-12. Variations on Pascal's Theorem. https://arxiv.org/abs/2411.07638

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