Nef Cone of a Generalized Kummer 4-fold

TL;DR

This paper computes the boundary of the movable and nef cones for a specific type of hyperkähler fourfold, the generalized Kummer 4-fold, associated with an abelian surface with rank 1 Néron-Severi group.

Contribution

It provides explicit calculations of the nef and movable cone boundaries for generalized Kummer 4-folds, advancing understanding of their birational geometry.

Findings

Boundary of nef cone explicitly determined

Boundary of movable cone explicitly determined

Results depend on the Néron-Severi rank of the abelian surface

Abstract

In this note, we calculate the boundary of movable cones and nef cones of the generalized Kummer 4-fold $\mathrm{Km}^2(A)$ attached to an abelian surface $A$ with $\mathrm{rkNS}(A) = 1$.