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

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.

17 pages, 4 figures, v. 5.0, the introduction is cleaned up, a reference to [KV] added