Cylinders in weak del Pezzo fibrations
Abstract
In this article, we shall look into the existence of vertical cylinders contained in a weak del Pezzo fibration as a generalization of the former work due to Dubouloz and Kishimoto in which they observed that of vertical cylinders found in del Pezzo fibrations. The essence lying in the existence of a cylinder in the generic fiber, we devote mainly ourselves into a geometry of minimal weak del Pezzo surfaces defined over a field of characteristic zero from the point of view of cylinders. As a result, we give the classification of minimal weak del Pezzo surfaces defined over a field of characteristic zero, moreover, we show that weak del Pezzo fibrations containing vertical cylinders are quite restrictive.
Cite
@article{arxiv.1912.09016,
title = {Cylinders in weak del Pezzo fibrations},
author = {Masatomo Sawahara},
journal= {arXiv preprint arXiv:1912.09016},
year = {2023}
}
Comments
21 pages; v3: Corrected some errors and revised based on the referee's suggestions; Accepted by Transform. Groups