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

Understand

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.