Year: 2025
Type: preprint
Abstract: 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 $p \ge 5$. 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.
Source: arXiv (Cornell University)
Authors: Ito, Hiroyuki, Takayashiki, Shota
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7077869447
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