The number of cubic surfaces with 27 lines over a finite field
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Dosyalar
Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
We determine the number of cubic surfaces with 27 lines over a finite field F-q. This is based on exploiting the relationship between non-conical six-arcs in a projective plane embedded in projective three-space and cubic surfaces with 27 lines. We revisit this classical relationship, which goes back to work of Clebsch in the nineteenth century. Our result can be used as an enumerative check for a computer classification of cubic surfaces with 27 lines over finite fields.
Açıklama
Anahtar Kelimeler
Geometry, Cubic surface, Finite field, Counting
Kaynak
Journal of Algebraic Combinatorics
WoS Q Değeri
Q3
Scopus Q Değeri
Q1
