∂∂-complex symplectic and Calabi-Yau manifolds: Albanese map, deformations and period maps

2017/11/14 by Anthes, Ben, Cattaneo, Andrea, Rollenske, Sönke +1
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1711.05107

Abstract

Let X be a compact complex manifold with trivial canonical bundle and satisfying the ∂∂-Lemma. We show that the Kuranishi space of X is a smooth universal deformation and that small deformations enjoy the same properties as X. If, in addition, X admits a complex symplectic form, then the local Torelli theorem holds and we obtain some information about the period map. We clarify the structure of such manifolds a little by showing that the Albanese map is a surjective submersion.

Related

• Applications of the affine structures on the Teichmüller spaces
• The ∂∂-lemma for general Clemens manifolds
• Irreducible symplectic complex spaces
• Hodge metric completion of the moduli space of Calabi-Yau manifolds
• Sections of Hodge bundles I: Global theory and applications to period maps