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Harmonic mappings of Kähler manifolds to locally symmetric spaces
© Publications mathématiques de l’I.H.É.S., 1989, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://Expand
Extensions of mixed Hodge structures
According to Deligne, the cohomology groups of a complex algebraic variety carry a generalized Hodge structure, or, in precise terms, a mixed Hodge structure [2]. The purpose of this paper is toExpand
The complex hyperbolic geometry of the moduli space of cubic surfaces
Recall that the moduli space of smooth (that is, stable) cubic curves is isomorphic to the quotient of the upper half plane by the group of fractional linear transformations with integerExpand
Period Mappings and Period Domains
Part I. Basic Theory of the Period Map: 1. Introductory examples 2. Cohomology of compact Kahler manifolds 3. Holomorphic invariants and cohomology 4. Cohomology of manifolds varying in a family 5.Expand
A Defect Relation for Equidimensional Holomorphic Mappings Between Algebraic Varieties
0. Introduction 1. Notations, terminology, and sign conventions (a) Line bundles and Chern classes (b) Currents and forms in C0 2. Construction of a volume form 3. A second main theorem forExpand
Infinitesimal variations of Hodge structure and the global Torelli problem
The aim of this report is to introduce the infinitesimal variation of Hodge structure as a tool for studying the global Torelli problem. Although our techniques have so far borne fruit only inExpand
The Millennium Prize Problems
A history of prizes in mathematics by J. Gray The Birch and Swinnerton-Dyer conjecture by A. Wiles The Hodge conjecture by P. Deligne Existence and smoothness of the Navier-Stokes equation by C. L.Expand
The Moduli Space of Cubic Threefolds As a Ball Quotient
The moduli space of cubic threefolds in $\mathbb{C}P^4$, with some minor birational modifications, is the Baily-Borel compactification of the quotient of the complex 10-ball by a discrete group. TheExpand
A complex hyperbolic structure for moduli of cubic surfaces
Abstract We show that the moduli space M of marked cubic surfaces is biholomorphic to ( B 4 − H )/Г, where B 4 is complex hyperbolic four-space, Γ is a specific group generated by complexExpand
Cubic surfaces with special periods
We show that the vector of period ratios of a cubic surface is rational over Q(ω), where ω = exp(2πi/3) if and only if the associate abelian variety is isogeneous to a product of Fermat ellipticExpand