Multiple Hilbert Transforms Associated With Polynomials

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Multiple Hilbert Transforms Associated with Polynomials

Author: Joonil Kim
language: en
Publisher: American Mathematical Soc.
Release Date: 2015-08-21
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The Fourier Transform for Certain HyperKahler Fourfolds

Author: Mingmin Shen
language: en
Publisher: American Mathematical Soc.
Release Date: 2016-03-10
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.
Irreducible Geometric Subgroups of Classical Algebraic Groups

Author: Timothy C. Burness,
language: en
Publisher: American Mathematical Soc.
Release Date: 2016-01-25
Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a non-trivial irreducible tensor-indecomposable -restricted rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where is a disconnected maximal positive-dimensional closed subgroup of preserving a natural geometric structure on .