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arXiv · 1309.5965

The Fourier transform for certain hyperKaehler fourfolds

Mingmin Shen·Charles Vial
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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.

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Mingmin Shen, Charles Vial. 2014-06-03. The Fourier transform for certain hyperKaehler fourfolds. https://arxiv.org/abs/1309.5965

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