The Fourier Transform For Certain Hyperkahler Fourfolds (memoirs Of The American Mathematical Society)
by Mingmin Shen /
2016 / English / PDF
1.4 MB Download
Using a codimension-$1$ algebraic cycle obtained from the Poincare
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 Beauville-Bogomolov class, the authors give
evidence for the existence of a similar decomposition for the Chow
ring of Hyperkahler 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.
Using a codimension-$1$ algebraic cycle obtained from the Poincare
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 Beauville-Bogomolov class, the authors give
evidence for the existence of a similar decomposition for the Chow
ring of Hyperkahler 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.
