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Moduli space of Calabi-Yau manifolds. (English) Zbl 0732.53056
Summary: We present an accessible account of the local geometry of the parameter space of Calabi-Yau manifolds. It is shown that the parameter space decomposes, at least locally, into a product with the space of parameters of the complex structure as one factor and a complex extension of the parameter space of the Kähler class as the other. It is also shown that each of these spaces is itself a Kähler manifold and is moreover a Kähler manifold of restricted type. There is a remarkable symmetry in the intrinsic structures of the two parameter spaces and the relevance of this to the conjectured existence of mirror manifolds is discussed. The two parameter spaces behave differently with respect to modular transformations and it is argued that the role of quantum corrections is to restore the symmetry between the two types of parameters so as to enforce modular invariance.
Reviewer: Reviewer (Berlin)

MSC:
53C55 Global differential geometry of Hermitian and Kählerian manifolds
53C80 Applications of global differential geometry to the sciences
58D27 Moduli problems for differential geometric structures
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