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We give a classification of components of the Hodge locus in any parameter space of smooth projective varieties.
L’analysis situs et la géométrie algébrique
S. Lefschetz · 1950
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On the differentiation of de Rham cohomology classes with respect to parameters
Nicholas M. Katz and Tadao Oda · 1968
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On the periods of certain rational integrals. I, II
Phillip A. Griffiths · 1969
Earlier work this paper cites.
The Hodge conjecture for cubic fourfolds
Steven Zucker · 1977
Earlier work this paper cites.
Infinitesimal variations of Hodge structure. I, II,III
James Carlson, Mark Green, Phillip Griffiths, and Joe Harris · 1983
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On the Noether-Lefschetz theorem and some remarks on codimension-two cycles
Phillip Griffiths and Joe Harris · 1985
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An introduction to infinitesimal variations of Hodge structures
Joe Harris · 1985
Earlier work this paper cites.
General components of the Noether-Lefschetz locus and their density in the space of all surfaces
Ciro Ciliberto, Joe Harris, and Rick Miranda · 1988
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Linear sections of determinantal varieties
David Eisenbud · 1988
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A new proof of the explicit Noether-Lefschetz theorem
Mark L. Green · 1988
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Une précision concernant le théorème de Noether
Claire Voisin · 1988
Cited alongside, same era.
Components of maximal dimension in the Noether-Lefschetz locus
Mark L. Green · 1989
Cited alongside, same era.
Composantes de petite codimension du lieu de Noether-Lefschetz
Claire Voisin · 1989
Cited alongside, same era.
The Noether-Lefschetz locus of regular elliptic surfaces with section and p g ≥ 2 p_{g}\geq 2
David A. Cox · 1990
Cited alongside, same era.
Le lieu de Noether-Lefschetz pour les variétés abéliennes
Olivier Debarre and Yves Laszlo · 1990
Cited alongside, same era.
Hodge theory and complex algebraic geometry. II
Claire Voisin · 2003
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A second-order invariant of the Noether-Lefschetz locus and two applications
Catriona Maclean · 2005
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Private letter
Pierre Deligne · 2009
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Multiple Integrals and Modular Differential Equations
Hossein Movasati · 2011
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Gromov-Witten theory and Noether-Lefschetz theory
Davesh Maulik and Rahul Pandharipande · 2012
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Quasi modular forms attached to Hodge structures
Hossein Movasati · 2013
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Sur le lieu de Noether-Lefschetz en degrés 6 6 et 7 7
Claire Voisin · 1990
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Contrexemple à une conjecture de J. Harris
Claire Voisin · 1991
Cited alongside, same era.
On the locus of Hodge classes
Eduardo H. Cattani, Pierre Deligne, and Aroldo G. Kaplan · 1995
Cited alongside, same era.
Algebraic Geometry
James Milne
Cited in the paper.
Hodge loci
Claire Voisin · 2013
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Gauss-Manin connection in disguise: Calabi-Yau threefolds
Murad Alim, Hossein Movasati, Emanuel Scheidegger, and Shing-Tung Yau · 2014
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Hypersurfaces in ℙ 5 \mathbb{P}^{5} containing unexpected subvarieties
Israel Vainsencher · 2014
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