Rational curves on O'Grady's tenfolds

TL;DR

This paper investigates the existence of uniruled divisors on O'Grady's tenfolds, demonstrating that certain polarized manifolds contain multiples of their polarization class that are uniruled divisors, advancing understanding of their geometric structure.

Contribution

It establishes the existence of uniruled divisors on specific deformation types of O'Grady's tenfolds, a new result in the study of their geometric properties.

Findings

Existence of uniruled divisors on polarized OG10 manifolds in certain moduli components

Multiple of polarization class can be realized as a uniruled divisor

Advances understanding of the geometry of 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.