Local and global theory of the moduli of polarized Calabi-Yau manifolds.

Título inglés	Local and global theory of the moduli of polarized Calabi-Yau manifolds.
Título español	Teoría local y global del espacio de moduli de las variedades polarizadas de Calabi-Yau.
Autor/es	Todorov, Andrey
Organización	Dep. Math. Univ. California, California, Estados Unidos;Bulgarian Acad. Sci. Inst. Math., Sofía, Bulgaria
Revista	0213-2230
Publicación	2003, 19(2): 687-730, 51 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	In this paper we review the moduli theory of polarized CY manifolds. We briefly sketched Kodaira-Spencer-Kuranishi local deformation theory developed by the author and G. Tian. We also construct the Teichmüller space of polarized CY manifolds following the ideas of I. R. Shafarevich and I. I. Piatetski-Shapiro. We review the fundamental result of E. Viehweg about the existence of the course moduli space of polarized CY manifolds as a quasi-projective variety. Recently S. Donaldson computed the moment map for the action of the group of symplectic diffeomorphisms on the space of Kiihler metrics with fixed class of cohomology. Combining this results with the solution of Calabi conjecture by Yau one obtains a very conceptual proof of the ...
Clasificación UNESCO	120101 ; 120402
Palabras clave español	Geometría algebraica ; Teoría de Hodge ; Espacio de moduli ; Variedades complejas ; Variedades kählerianas
Código MathReviews	MR2023203
Código Z-Math	Zbl 1058.32019
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