Geometry and arithmetic of geometrically integral regular del Pezzo surfaces
Algebraic Geometry
2025-11-12 v3
Abstract
We classify geometrically integral regular del Pezzo surfaces which are not geometrically normal over imperfect fields of positive characteristic. Based on this classification, we show that a three-dimensional terminal del Pezzo fibration onto a curve over an algebraically closed field always admits a section. Moreover, we prove that the total space is rational if the base curve is rational and the anticanonical degree of a fibre is at least five.
Keywords
Cite
@article{arxiv.2408.11378,
title = {Geometry and arithmetic of geometrically integral regular del Pezzo surfaces},
author = {Fabio Bernasconi and Hiromu Tanaka},
journal= {arXiv preprint arXiv:2408.11378},
year = {2025}
}
Comments
v3: 40 pages, to appear in Algebra & Number Theory