Weak positivity and the stability of certain Hilbert points (Q909728)

The author's aim in this paper is to use the notion of weak positivity and other methods from classification theory to construct quasi- projective coarse moduli schemes. In fact he obtains only a partial result, namely that smooth points of the reduced Hilbert schemes of canonically polarised manifolds are stable in the sense of geometric invariant theory; in particular, if such a reduced Hilbert scheme is actually non-singular, then the corresponding coarse moduli space exists and is quasi-projective. The techniques are also applied to fibre spaces, leading in particular to a simplified proof of the generalised Iitaka conjecture \(C^+_{n,m}\).