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arXiv · 1301.7235

Progrès récents sur les fonctions normales (d'après Green-Griffiths, Brosnan-Pearlstein, M. Saito, Schnell...)

François Charles
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Abstract

Given a family of smooth complex projective varieties, the Hodge conjecture predicts the algebraicity of the locus of Hodge classes. This was proven unconditionnally by Cattani, Deligne and Kaplan in 1995. In a similar way, conjectures on algebraic cycles have led Green and Griffiths to conjecture the algebraicity of the zero locus of normal functions. This corresponds to a mixed version of the theorem of Cattani, Deligne and Kaplan. This result has been proven recently by Brosnan-Pearlstein, Kato-Nakayama-Usui, and Schnell building on work of M. Saito. We will present some of the ideas around this theorem.

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François Charles. 2013-01-30. Progrès récents sur les fonctions normales (d'après Green-Griffiths, Brosnan-Pearlstein, M. Saito, Schnell...). https://arxiv.org/abs/1301.7235

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