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arXiv · 2408.11378

Geometry and arithmetic of geometrically integral regular del Pezzo surfaces

Fabio Bernasconi·Hiromu Tanaka
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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.

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Fabio Bernasconi, Hiromu Tanaka. 2024-08-21. Geometry and arithmetic of geometrically integral regular del Pezzo surfaces. https://arxiv.org/abs/2408.11378

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