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OverviewUsing 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. Full Product DetailsAuthor: Mingmin Shen , Charles VialPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.319kg ISBN: 9781470417406ISBN 10: 1470417405 Pages: 161 Publication Date: 30 April 2016 Audience: Professional and scholarly , Professional and scholarly , Professional & Vocational , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsIntroduction The Fourier transform for HyperKahler fourfolds The Cohomological Fourier Transform The Fourier transform on the Chow groups of HyperKahler fourfolds The Fourier decomposition is motivic First multiplicative results An application to symplectic automorphisms On the birational invariance of the Fourier decomposition An alternate approach to the Fourier decomposition on the Chow ring of Abelian varieties Multiplicative Chow-Kunneth decompositions Algebraicity of $\mathfrak{B}$ for HyperKahler varieties of $\mathrm{K3}^{[n]}$-type The Hilbert Scheme $S^{[2]}$ Basics on the Hilbert scheme of Length-$2$ subschemes on a variety $X$ The incidence correspondence $I$ Decomposition results on the Chow groups of $X^{[2]}$ Multiplicative Chow-Kunneth decomposition for $X^{[2]}$ The Fourier decomposition for $S^{[2]}$ The Fourier decomposition for $S^{[2]}$ is multiplicative The Cycle $L$ of $S^{[2]}$ via moduli of stable sheaves The variety of lines on a cubic fourfold The incidence correspondence $I$ The rational self-map $\varphi : F \dashrightarrow F$ The Fourier decomposition for $F$ A first multiplicative result The rational self-map $\varphi :F\dashrightarrow F$ and the Fourier decomposition The Fourier decomposition for $F$ is multiplicative Appendix A. Some geometry of cubic fourfolds Appendix B. Rational maps and Chow groups ReferencesReviewsAuthor InformationMingmin Shen, Korteweg-de Vries Institute for Mathematics, University of Amsterdam, The Netherlands. Charles Vial, University of Cambridge, United Kingdom. Tab Content 6Author Website:Countries AvailableAll regions |
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