2013/01/30 by François Charles, Charles, François
Arts and Humanities · Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #French Historical and Cultural Studies #Geometry and complex manifolds #Historical Studies and Socio-cultural Analysis #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1301.7235
openalex publication_date 2013/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a family of smooth complex projective varieties, the Hodge conjecture\npredicts the algebraicity of the locus of Hodge classes. This was proven\nunconditionnally by Cattani, Deligne and Kaplan in 1995. In a similar way,\nconjectures on algebraic cycles have led Green and Griffiths to conjecture the\nalgebraicity of the zero locus of normal functions. This corresponds to a mixed\nversion of the theorem of Cattani, Deligne and Kaplan. This result has been\nproven recently by Brosnan-Pearlstein, Kato-Nakayama-Usui, and Schnell building\non work of M. Saito. We will present some of the ideas around this theorem.\n