Base divisors of big and nef line bundles on irreducible symplectic varieties

TL;DR

This paper characterizes the base divisors of big and nef line bundles on irreducible symplectic varieties, showing they are irreducible and reduced, and studies their behavior under deformation for specific types.

Contribution

It provides a description of base divisors for big and nef line bundles on irreducible symplectic varieties, extending understanding of their geometric properties.

Findings

Base divisors are always irreducible and reduced.

Description applies under certain deformation conditions.

Behavior of divisorial base components is analyzed for specific types.

Abstract

Under some conditions on the deformation type, which we expect to be satisfied for arbitrary irreducible symplectic varieties, we describe which big and nef line bundles on irreducible symplectic varieties have base divisors. In particular, we show that such base divisors are always irreducible and reduced. This is applied to understand the behaviour of divisorial base components of big and nef line bundles under deformations and for K3$^{[n]}$-type and Kum$^n$-type.