Rational curves on O’Grady’s tenfolds

Abstract

We study the existence of ample uniruled divisors on irreducible holomorphic symplectic manifolds that are deformations of the 10-dimensional example introduced by O’Grady. In particular, we show that for any polarized O’Grady’s 10-dimensional ($OG10$) 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.