The Fourier transform for certain hyperKaehler fourfolds

2013/09/23 by Mingmin Shen, Shen, Mingmin, Charles Vial +1 · 4 citations
Mathematics · #14C15 #14C17 #14C25 #14J28 #14J32 #14K99 #53C26 #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.1309.5965

openalex publication_date 2013/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using a codimension-1 algebraic cycle obtained from the Poincaré line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety A and showed that the Fourier transform induces a decomposition of the Chow ring CH^*(A). By using a codimension-2 algebraic cycle representing the Beauville--Bogomolov class, we give evidence for the existence of a similar decomposition for the Chow ring of hyperKähler varieties deformation equivalent to the Hilbert scheme of length-2 subschemes on a K3 surface. We indeed establish the existence of such a decomposition for the Hilbert scheme of length-2 subschemes on a K3 surface and for the variety of lines on a very general cubic fourfold.

Citations

• On a conjectural filtration on the Chow groups of an algebraic variety

Cited by

• Questions on the Chow ring of complete intersections
• Motivic multiplicativity of complete intersections
• Birational Chow-Künneth decompositions
• Hyperkahler manifolds of Jacobian type
• K3 categories, one-cycles on cubic fourfolds, and the Beauville-Voisin filtration

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