On the ACC for lengths of extremal rays

TL;DR

This paper proves that the lengths of extremal rays in certain toric Fano varieties with specific properties follow the ascending chain condition, contributing to the understanding of their geometric structure.

Contribution

It establishes the ascending chain condition for extremal ray lengths in n-dimensional Q-factorial toric Fano varieties with Picard number one, a new result in algebraic geometry.

Findings

Lengths of extremal rays satisfy the ascending chain condition

Applicable to n-dimensional Q-factorial toric Fano varieties

Advances understanding of extremal ray structures in algebraic geometry

Abstract

We discuss the ascending chain condition for lengths of extremal rays. We prove that the lengths of extremal rays of $n$-dimensional $\mathbb Q$-factorial toric Fano varieties with Picard number one satisfy the ascending chain condition.