Classification of flocks of the quadratic cone in PG(3,64) release_voi5zg4f7vajvdt6ko7mks65va

by Giusy Monzillo, Tim Penttila, Alessandro Siciliano

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2022  

Abstract

Flocks are an important topic in the field of finite geometry, with many relations with other objects of interest. This paper is a contribution to the difficult problem of classifying flocks up to projective equivalence. We complete the classification of flocks of the quadratic cone in PG(3,q) for q <= 71, by showing by computer that there are exactly three flocks of the quadratic cone in PG(3,64), up to equivalence. The three flocks had previously been discovered, and they are the linear flock, the Subiaco flock and the Adelaide flock. The classification proceeds via the connection between flocks and herds of ovals in PG(2,q), q even, and uses the prior classification of hyperovals in PG(2,64).
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Date   2022-05-11
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arXiv  2205.05344v1
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