Fano manifolds of index n-2 and the cone conjecture

TL;DR

This paper investigates the Morrison--Kawamata Cone Conjecture for blowups of Fano manifolds with index n-2, extending previous work on index n-1 cases to a broader class of Fano manifolds.

Contribution

It extends the verification of the Morrison--Kawamata Cone Conjecture to blowups of Fano manifolds of index n-2, broadening the class of manifolds for which the conjecture is confirmed.

Findings

Confirmed the conjecture for certain blowups of Fano manifolds of index n-2.

Extended previous results from index n-1 to index n-2 cases.

Provided new insights into the structure of nef and movable cones in these manifolds.

Abstract

The Morrison--Kawamata Cone Conjecture predicts that the action of the automorphism group on the effective nef cone and the action of the pseudo-automorphism group on the effective movable cone of a klt Calabi-Yau pair have rational, polyhedral fundamental domains. In a previous paper, we proved the conjecture for certain blowups of Fano manifolds of index n-1. In this paper, we consider the Morrison--Kawamata conjecture for blowups of Fano manifolds of index n-2.