The Fourier transform for certain hyperKaehler fourfolds

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 $C{H}^{\ast }(A)$. 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.

Final version, 104 pages. Accepted at Memoirs of the AMS

References in corpus (3)

• On the Chow ring of birational irreducible symplectic varieties
• Symplectic automorphisms of K3 surfaces of arbitrary order
• Surfaces with involution and Prym constructions

Cited by in corpus (7)

• On the Chow ring of Cynk-Hulek Calabi-Yau varieties and Schreieder varieties
• Exceptional collections, and the Neron-Severi lattice for surfaces
• Derived categories of K3 surfaces, O'Grady's filtration, and zero-cycles on holomorphic symplectic varieties
• K3 categories, one-cycles on cubic fourfolds, and the Beauville-Voisin filtration
• Triangle varieties and surface decomposition of hyper-Kähler manifolds
• Hyperkahler manifolds of Jacobian type
• Birational Chow-Künneth decompositions