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 $CH^*(A)$. By using a codimension$2$ algebraic cycle representing the BeauvilleBogomolov 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2013
 arXiv:
 arXiv:1309.5965
 Bibcode:
 2013arXiv1309.5965S
 Keywords:

 Mathematics  Algebraic Geometry;
 14C25;
 14C15;
 53C26;
 14J28;
 14J32;
 14K99;
 14C17
 EPrint:
 Final version, 104 pages. Accepted at Memoirs of the AMS