The Fourier Transform for Certain HyperKähler Fourfolds

By M. Shen, Charles Vial. Memoirs of the American Mathematical Society, 2013

137 citations recorded by the source corpus.

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 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 hyperKahler 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/46e4aadbb7e836d854e55373e8ca2a2f96b22822

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. M. Shen
2. L. Fu
3. Charles Vial
4. Zhiyu Tian

In Mathematical Physics

1. M. Shen
2. L. Fu
3. Charles Vial
4. Zhiyu Tian

Citations in the corpus

• Motivic hyper-Kähler resolution conjecture, I : Generalized Kummer varieties (2016, background): “Let us first of all introduce the following notion, which was introduced in [53] and which avoids any mentions to the Bloch– Beilinson conjecture.”
• THE MOTIVE OF THE HILBERT CUBE $X^{[3]}$ (2015, background): “The case of the Hilbert square was taken care of in [12].”