Hodge conjecture for projective hypersurface

2023/12/14 by Bouali, Johann
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.09268

Abstract

We show that a Hodge class of a complex smooth projective hypersurface is an analytic logarithmic De Rham class. On the other hand we show that for a complex smooth projective variety an analytic logarithmic De Rham class of of type (d,d) is the class of codimension d algebraic cycle. We deduce the Hodge conjecture for smooth projective hypersurfaces.

Related

• De Rham logarithmic classes and Tate conjecture
• Degeneration of families of projective hypersurfaces and Hodge conjecture
• The Hodge structure on the singularity category of a complex hypersurface
• A Solution to the Hodge Conjecture
• The Generalized Hodge conjecture for 1-cycles and codimension two algebraic cycles