Any component of moduli of polarized hyperkaehler manifolds is dense in its deformation space

TL;DR

This paper proves that for hyperkähler manifolds, the set of algebraic deformations polarized by a given class is dense in the moduli space, highlighting the richness of algebraic structures within the deformation space.

Contribution

It establishes the density of divisors associated with polarization classes in the moduli space of hyperkähler manifolds, extending understanding of their deformation theory.

Findings

Divisors of polarized hyperkähler manifolds are dense in the moduli space.

Every positive integer class in cohomology defines a dense subset.

The result applies to all connected components of these divisors.

Abstract

Let M be a compact hyperkaehler manifold, and W the coarse moduli of complex deformations of M. Every positive integer class v in $H^2(M)$ defines a divisor $D_v$ in W consisting of all algebraic manifolds polarized by v. We prove that every connected component of this divisor is dense in W.