On Fano varieties with torus action of complexity one

TL;DR

This paper classifies certain Fano varieties with a one-dimensional torus action, providing bounds and invariants based on dimension and Picard index, extending previous classifications.

Contribution

It offers effective bounds and classification results for rational $ ext{Q}$-factorial Fano varieties with complexity-one torus action and Picard number one, generalizing earlier work.

Findings

Provides bounds depending on invariants

Classifies varieties based on dimension and Picard index

Extends previous classifications to new cases

Abstract

In this work we provide effective bounds and classification results for rational $\QQ$-factorial Fano varieties with a complexity-one torus action and Picard number one depending on the invariants dimension and Picard index. This complements earlier work by Hausen, S\"u{\ss} and the author, where the case of free divisor class group of rank one was treated.