Rational curves on primitive symplectic varieties of OG6 singular type

TL;DR

This paper proves that on certain primitive symplectic varieties related to OG6, ample classes are proportional to uniruled divisors, extending previous results and answering a specific open question in the field.

Contribution

It establishes a proportionality between ample classes and uniruled divisors on primitive symplectic varieties of OG6 type, generalizing prior work to a broader class.

Findings

Ample classes are proportional to uniruled divisors on these varieties.

The result extends previous theorems to new deformation types.

Answers an open question posed by Lehn, Mongardi, and Pacienza.

Abstract

We prove that any ample class on a primitive symplectic variety that is locally trivial deformation of O'Grady's singular 6 dimensional example is proportional to the first Chern class of a uniruled divisor. This result answers a question of Lehn, Mongardi and Pacienza, extending their result for primitive symplectic varieties of this deformation type.