Betten
Anton
https://scigraph.springernature.com/explorer/license/
2019-04
https://link.springer.com/10.1007%2Fs10623-018-0590-2
931-953
2019-04-11T14:02
en
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.
research_article
Cubic surfaces over small finite fields
false
2019-04-01
articles
Department of Mathematics, Colorado State University, 80523, Fort Collins, CO, USA
Colorado State University
Karaoglu
Fatma
dimensions_id
pub.1110283325
1573-7586
Designs, Codes and Cryptography
0925-1022
Springer Nature - SN SciGraph project
10.1007/s10623-018-0590-2
doi
Pure Mathematics
957488941a823e1774739c01c95cff4bd98ced9521b2fea6fa8fc817f3ada2bf
readcube_id
Department of Mathematics, University of Sussex, BN1 9QH, Brighton, UK
University of Sussex
87
4
Mathematical Sciences