Geometry and arithmetic of geometrically integral regular del Pezzo surfaces

Fuente: arXiv
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Main Authors: Bernasconi, Fabio, Tanaka, Hiromu
Format: Preprint
Published: 2024
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_version_ 1866909897002582016
author Bernasconi, Fabio
Tanaka, Hiromu
author_facet Bernasconi, Fabio
Tanaka, Hiromu
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2408_11378
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Geometry and arithmetic of geometrically integral regular del Pezzo surfaces
Bernasconi, Fabio
Tanaka, Hiromu
Algebraic Geometry
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.
title Geometry and arithmetic of geometrically integral regular del Pezzo surfaces
topic Algebraic Geometry
url https://arxiv.org/abs/2408.11378