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We give a characterizaton of smooth ample Hypersurfaces in Abelian Varieties and also describe an irreducible connected component of their moduli space: it consists of the Hypersurfaces of a given polarization type, plus the iterated univariate coverings of normal type (of the same polarization type). The above manifolds yield also a connected component of the open set of Teichmuller space consisting of Kahler complex structures.
We present an algorithm for explicitly computing the number of generators of the stable cohomology algebra of any rationally smooth partial toroidal compactification of ${mathcal A}_g$, satisfying certain additivity and finiteness properties, in term
We describe the birational and the biregular theory of cyclic and Abelian coverings between real varieties.
Let M be the moduli scheme of canonically polarized manifolds with Hilbert polynomial h. We construct for a given finite set I of natural numbers m>1 with h(m)>0 a projective compactification M of the reduced scheme underlying M such that the ample i
We consider the family $mathrm{MP}_d$ of affine conjugacy classes of polynomial maps of one complex variable with degree $d geq 2$, and study the map $Phi_d:mathrm{MP}_dto widetilde{Lambda}_d subset mathbb{C}^d / mathfrak{S}_d$ which maps each $f in
Faltings proved that there are finitely many abelian varieties of genus $g$ of a number field $K$, with good reduction outside a finite set of primes $S$. Fixing one of these abelian varieties $A$, we prove that there are finitely many smooth hypersu