Rational curves on O'Grady's tenfolds

Abstract

We study the existence of ample uniruled divisors on irreducible holomorphic symplectic manifolds that are deformation of the ten dimensional example introduced by O'Grady. In particular, we show that for any polarized OG10 manifold lying in four specific connected components of the moduli space of polarized OG10 manifolds there exists a multiple of the polarization that is the class of a uniruled divisor.