Flops on holomorphic symplectic fourfolds and determinantal cubic hypersurfaces

TL;DR

This paper investigates the birational geometry of certain holomorphic symplectic fourfolds derived from cubic fourfolds, focusing on cone structures and automorphisms that influence their geometric classification.

Contribution

It provides explicit computations of the ample and moving cones and identifies a birational automorphism of infinite order, advancing understanding of these varieties' birational properties.

Findings

Computed the ample and moving cones of the varieties.

Identified a birational automorphism of infinite order.

Explained the chamber decomposition of the moving cone.

Abstract

We study the birational geometry of irreducible holomorphic symplectic varieties arising as varieties of lines of general cubic fourfolds containing a cubic scroll. We compute the ample and moving cones, and exhibit a birational automorphism of infinite order explaining the chamber decomposition of the moving cone.