Numbers of points of surfaces in the projective 3-space over finite fields

2014/09/20 by Homma, Masaaki, Kim, Seon Jeong · 1 citation
#14G15 #14J70 #14N05 #14N15 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1409.5842

Abstract

In the previous paper, we established an elementary bound for numbers of points of surfaces in the projective 3-space over \Bbb F_q. In this paper, we give the complete list of surfaces that attain the elementary bound. Precisely those surfaces are the hyperbolic surface, the nonsingular Hermitian surface, and the surface of minimum degree containing all \Bbb F_q-points of the 3-space.

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