A remark on the non-rationality Problem for generic cubic fourfolds

2006/10/31 by Kulikov, Vik. S.
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0610963

Abstract

It is proved that the non-rationality of a generic cubic fourfold follows from a conjecture on the non-decomposability in the direct sum of non-trivial polarized Hodge structures of the polarized Hodge structure on transcendental cycles on a projective surface.

Related

• On the rationality and the finite dimensionality of a cubic fourfold
• A remark on algebraic cycles on cubic fourfolds
• A new proof of the nonrationality of cubic threefolds
• Cubic fourfolds, K3 surfaces, and rationality questions
• On lattice polarizable cubic fourfolds