An affine local criterion for toric projective space bundles

Osamu Fujino, Hiroshi Sato

Abstract

We study when an equidimensional toric morphism is forced to be a projective-space bundle. Our main result is an affine rigidity theorem: if the base space is affine, the toric relative canonical divisor is $\mathbb Q$-Cartier, and its negative has degree greater than the relative dimension on every complete curve, then the morphism is equivariantly a trivial projective-space bundle. As an application, we derive a projective-space-bundle theorem for equidimensional toric contractions associated to long extremal rays, without assuming $\mathbb Q$-factoriality.

Disclosure

“imension. Acknowledgments. The first author was partially supported by JSPS KAKENHI Grant Number JP23K20787. The second author was partially supported by JSPS KAKENHI Grant Number 24K06679. The authors acknowledge the use of Rethlas and ChatGPT during the development of this work. These tools were used in the exploratory phase of the research, including discussions of formulations and the construction of examples. All mathematical arguments, proofs, and final verifications were c”
PDF page 2

Classification: Suggesting mathematical examples or conjectures
Multiplier: 6
Verified: 2026-08-23T05:09:34.581200Z

Structural counts

Pages 15 pdf

Theorems 2 source

Lemmas 6 source

Propositions 1 source

Corollaries 1 source

Definitions 0 source

Displayed equations 147 source

Bibliography entries 10 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file toricPdbdl.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.