Bounds on the Picard rank of toric Fano varieties with minimal curve constraints-Reference-Cited by-同舟云学术

Bounds on the Picard rank of toric Fano varieties with minimal curve constraints

Published:2023-01-30 Issue: Volume: Page:
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Beheshti R.,Wormleighton B.

Abstract

We study the Picard rank of smooth toric Fano varieties constrained to possess families of minimal rational curves of given degree. We discuss variants of a conjecture of Chen–Fu–Hwang and prove a version of their statement that recovers the original conjecture in sufficiently high dimension. We also prove new cases of the original conjecture for high degrees in all dimensions. Our main tools come from toric Mori theory and the combinatorics of Fano polytopes.

Funder

National Science Foundation

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/proc/0000-000-00/S0002-9939-2023-16267-X/proc16267_AM.pdf

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