The Fourier Transform for Certain HyperKahler Fourfolds
- ISBN-10
- 1470417405
- ISBN-13
- 9781470417406
- Category
- Fourier transformations
- Pages
- 161
- Language
- English
- Published
- 2016-03-10
- Publisher
- American Mathematical Soc.
- Authors
- Mingmin Shen, Charles Vial
Description
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, 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.
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