Seminar

I shall consider in my talk ample and smooth hypersurfaces X contained in an Abelian variety A, and compact Kaehler manifolds which are topologically equivalent to X, or have the same cohomology (this case is a special one of the more general investigation of Inoue type Varieties, initiated in joint work with Ingrid Bauer). The main result, (joint work with Yongnam Lee) is the description of an irreducible connected component of the moduli space (and of the Kaehler-Teichmueller space), formed by the hypersurfaces with a given polarization type, and by the iterated univariate coverings of normal type. I shall illustrate, in sketching the proof, a quite general result on deformation to hypersurface embedding. Time permitting, I shall also discuss some results and conjectures related to the behaviour of the canonical map for general such Hypersurfaces X.