Algebraic cycles on the Fano variety of lines of a cubic fourfold

2016/09/19 by Kalyan Banerjee, Banerjee, Kalyan · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1609.05627

openalex publication_date 2016/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this text we prove that if a smooth cubic in \PR⁵ has its Fano variety of lines birational to the Hilbert scheme of two points on a K3 surface, then there exists a smooth projective curve or a smooth projective surface embedded in the Fano variety, such that the kernel of the push-forward (at the level of zero cycles ) induced by the closed embedding is torsion.

Cited by

• On the rationality and the finite dimensionality of a cubic fourfold

Related

• Algebraic cycles on Fano varieties of some cubics
• Hilbert schemes of two points on K3 surfaces and certain rational cubic fourfolds
• Fano varieties of cubic fourfolds containing a plane
• Singularities of Fano varieties of lines on singular cubic fourfolds
• Lines on cubic threefolds and fourfolds containing a plane