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

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

2010-08-14

arxiv.org/abs/1008.2480v4

Mathematics

Algebraic Geometry

17 pages, 4 figures, v. 4.0, added an extra proposition about non-positive vectors in H^2, proofs cleaned up

Scientific paper

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.

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