The cone conjecture for some rational elliptic threefolds

TL;DR

This paper verifies the Morrison--Kawamata conjecture for a specific class of rational threefolds, expanding the understanding of the conjecture in the context of klt Calabi--Yau pairs in three dimensions.

Contribution

It provides the first verified case of the conjecture for klt Calabi--Yau pairs in dimension 3 with a non-zero boundary divisor.

Findings

Confirmed the conjecture for blowups of P^3 in the base locus of a net of quadrics

First verification of the conjecture for certain klt Calabi--Yau pairs in dimension 3

Advances understanding of the Morrison--Kawamata conjecture in algebraic geometry

Abstract

We verify the Morrison--Kawamata conjecture for a certain class of rational threefolds, namely blowups of P^3 in the base locus of a net of quadrics with no reducible members. This seems to be the first verified case of the conjecture for klt Calabi--Yau pairs in dimension 3 with non-zero boundary divisor.