Rational curves on primitive symplectic varieties of OG6 singular type

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-Pacienza [LMP21, Remark 4.7], extending their result [LMP21, Theorem 1.3] for primitive symplectic varieties of this deformation type. 2020 Mathematics Subject Classification. 14C99 (14J40 ).