2025/08/25 by Ito, Hiroyuki, Takayashiki, Shota
#11G30 #14D06 #14G17 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2508.17790
As a generalization of a quasi-elliptic surface, there is a quasi-hyperelliptic surface, a nonsingular projective surface which has a fibration structure whose general fiber is a quasi-hyperelliptic curve (= singular hyperelliptic curve with one cuspidal singular point) of genus (p-1)/2 in characteristic p ≥ 5. In this paper, we consider unirational quasi-hyperelliptic surfaces in characteristic 5, and classify singular fibers and give a formula for the arithmetic genus and the self-intersection number of the canonical divisor. As a corollary, we classify rational quasi-hyperelliptic surfaces by determining the combinations of singular fibers, the defining equations and sections.