Inverse curve problems on del Pezzo surfaces
Algebraic Geometry
2025-11-13 v1 Number Theory
Abstract
We classify the number of -rational lines and conic fibrations on del Pezzo surfaces over a field in terms of relatively minimal surfaces and establish rational curve analogues of the inverse Galois problem for del Pezzo surfaces. We completely solve these problems in all degrees over all global, local and finite fields and provide new solutions of the inverse Galois problem in characteristic 2. Our results generalise well-known theorems on cubic surfaces.
Cite
@article{arxiv.2511.08688,
title = {Inverse curve problems on del Pezzo surfaces},
author = {Enis Kaya and Stephen McKean and Sam Streeter and H. Uppal},
journal= {arXiv preprint arXiv:2511.08688},
year = {2025}
}
Comments
66 pages, comments welcome