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The Fourier Transform for Certain HyperKähler Fourfolds
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The Fourier Transform for Certain HyperKähler Fourfolds
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eBook
The Fourier Transform for Certain HyperKähler Fourfolds
2016
Overview
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 \\mathrm{CH}^*(A). By using a codimension-2 algebraic cycle representing the Beauvilleâe\"Bogomolov class, the authors 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. They 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.
Publisher
American Mathematical Society
ISBN
9781470417406, 1470417405
