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arXiv · 2401.08800

Generalized Eckardt points on del Pezzo surfaces of degree 1

Julie Desjardins·Yu Fu·Kelly Isham·Rosa Winter
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Abstract

We study intersections of exceptional curves on del Pezzo surfaces of degree 1, motivated by questions in arithmetic geometry. Outside characteristics 2 and 3, at most 10 exceptional curves can intersect in a point. We classify the different ways in which 10 exceptional curves can intersect, construct a new family of surfaces with 10 exceptional curves intersecting in a point, and discuss strategies for finding more such examples.

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Julie Desjardins, Yu Fu, Kelly Isham, Rosa Winter. 2025-10-17. Generalized Eckardt points on del Pezzo surfaces of degree 1. https://arxiv.org/abs/2401.08800

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