Cubic surfaces over small finite fields View Full Text


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Article Info

DATE

2019-04

AUTHORS

Anton Betten, Fatma Karaoglu

ABSTRACT

In the 1960s, Hirschfeld embarked on a program to classify cubic surfaces with 27 lines over finite fields. This work is a contribution to this problem. We develop an algorithm to classify surfaces with 27 lines over a finite field using the classical theory of double-sixes. This algorithm is used to classify these surfaces over all fields of order q at most 97. We then construct a family of cubic surfaces over finite fields of odd order. The generic surfaces in this family have six Eckardt points and they are invariant under a symmetric group of degree four. The family turns out to be isomorphic to the example of a family of cubic surface given over the real numbers by Hilbert and Cohn-Vossen. More... »

PAGES

931-953

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10623-018-0590-2

DOI

http://dx.doi.org/10.1007/s10623-018-0590-2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1110283325


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