The Moduli Space of smooth Ample Hypersurfaces in Abelian Varieties

2019/03/18 by Catanese, Fabrizio, Lee, Yongnam
#14D15 #14J15 #14J70 #14K12 #32G05 #32G10 #32H02 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.07764

Abstract

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 Teichmüller space consisting of Kähler complex structures.

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