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

Todorov, Andrey. "Local and global theory of the moduli of polarized Calabi-Yau manifolds.." Revista Matemática Iberoamericana 19.2 (2003): 687-730. <http://eudml.org/doc/39709>.

@article{Todorov2003,
abstract = {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 ...},
author = {Todorov, Andrey},
journal = {Revista Matemática Iberoamericana},
keywords = {Geometría algebraica; Teoría de Hodge; Espacio de moduli; Variedades complejas; Variedades kählerianas; Calabi-Yau manifolds; Teichmüller spaces; moduli spaces},
language = {eng},
number = {2},
pages = {687-730},
title = {Local and global theory of the moduli of polarized Calabi-Yau manifolds.},
url = {http://eudml.org/doc/39709},
volume = {19},
year = {2003},
}

TY - JOUR
AU - Todorov, Andrey
TI - Local and global theory of the moduli of polarized Calabi-Yau manifolds.
JO - Revista Matemática Iberoamericana
PY - 2003
VL - 19
IS - 2
SP - 687
EP - 730
AB - 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 ...
LA - eng
KW - Geometría algebraica; Teoría de Hodge; Espacio de moduli; Variedades complejas; Variedades kählerianas; Calabi-Yau manifolds; Teichmüller spaces; moduli spaces
UR - http://eudml.org/doc/39709
ER -