On the Cone conjecture for Calabi-Yau manifolds with Picard number two

TL;DR

This paper explicitly computes automorphism groups of certain Calabi-Yau manifolds with Picard number two and proves the Cone conjecture holds when the birational automorphism group is infinite.

Contribution

It provides explicit calculations of automorphism groups and verifies the Cone conjecture for a specific class of Calabi-Yau manifolds with Picard number two.

Findings

Automorphism groups are explicitly calculated.

The Cone conjecture is proven when the birational automorphism group is infinite.

Supports the validity of the Cone conjecture in new cases.

Abstract

Following a recent work of Oguiso, we calculate explicitly the groups of automorphisms and birational automorphisms on a Calabi-Yau manifold with Picard number two. When the group of birational automorphisms is infinite, we prove that the Cone conjecture of Morrison and Kawamata holds.