Remarks on hypersurfaces in $\mathbf{P}^1\times Z$
Algebraic Geometry
2026-05-29 v1 Commutative Algebra
Abstract
We study the birational geometry of hypersurfaces in projective varieties of the form , where satisfies mild assumptions. Building on recent results of Herrera--Laface--Ugaglia, we study their Cox rings (when finitely generated) in terms of the Cox ring of . In particular, we obtain a complete picture when is a Fano variety of dimension at least 3, and with class group of rank 1.
Cite
@article{arxiv.2605.29515,
title = {Remarks on hypersurfaces in $\mathbf{P}^1\times Z$},
author = {Francesco Antonio Denisi and Antonio Laface},
journal= {arXiv preprint arXiv:2605.29515},
year = {2026}
}
Comments
v1, 12 pages. Comments are welcome!