Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8895627 | Finite Fields and Their Applications | 2018 | 18 Pages |
Abstract
In this paper, we characterize all curves over Fq arising from a plane sectionP:X3âe0X0âe1X1âe2X2=0 of the Fermat surfaceS:X0d+X1d+X2d+X3d=0, where q=ph=2d+1 is a prime power, p>3, and e0,e1,e2âFq. In particular, we prove that any nonlinear component GâPâ©S is a smooth classical curve of degree n⩽d attaining the Stöhr-Voloch bound#G(Fq)⩽12n(n+qâ1)â12i(nâ2), with iâ{0,1,2,3,n,3n}.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Herivelto Borges, Gary Cook, Mariana Coutinho,