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The Fourier Transform for Certain HyperKähler Fourfolds
About this Title
Mingmin Shen, Korteweg-de Vries Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090GE, Amsterdam, Netherlands and Charles Vial, DPMMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
Publication: Memoirs of the American Mathematical Society
Publication Year:
2016; Volume 240, Number 1139
ISBNs: 978-1-4704-1740-6 (print); 978-1-4704-2830-3 (online)
DOI: https://doi.org/10.1090/memo/1139
Published electronically: November 18, 2015
Keywords: HyperKähler manifolds,
irreducible holomorphic symplectic varieties,
cubic fourfolds,
Fano schemes of lines,
K3 surfaces,
Hilbert schemes of points,
Abelian varieties,
motives,
algebraic cycles,
Chow groups,
Chow ring,
Chow–Künneth decomposition,
Bloch–Beilinson filtration,
modified diagonals
MSC: Primary 14C25, 14C15, 53C26, 14J28, 14J32, 14K99, 14C17
Table of Contents
Chapters
- Introduction
1. The Fourier Transform for HyperKähler Fourfolds
- 1. The Cohomological Fourier Transform
- 2. The Fourier Transform on the Chow Groups of HyperKähler Fourfolds
- 3. The Fourier Decomposition Is Motivic
- 4. First Multiplicative Results
- 5. An Application to Symplectic Automorphisms
- 6. On the Birational Invariance of the Fourier Decomposition
- 7. An Alternate Approach to the Fourier Decomposition on the Chow Ring of Abelian Varieties
- 8. Multiplicative Chow–Künneth Decompositions
- 9. Algebraicity of $\mathfrak {B}$ for HyperKähler Varieties of $\mathrm {K3}^{[n]}$-type
2. The Hilbert Scheme $S^{[2]}$
- 10. Basics on the Hilbert Scheme of Length-$2$ Subschemes on a Variety $X$
- 11. The Incidence Correspondence $I$
- 12. Decomposition Results on the Chow Groups of $X^{[2]}$
- 13. Multiplicative Chow–Künneth Decomposition for $X^{[2]}$
- 14. The Fourier Decomposition for $S^{[2]}$
- 15. The Fourier Decomposition for $S^{[2]}$ is Multiplicative
- 16. The Cycle $L$ of $S^{[2]}$ via Moduli of Stable Sheaves
3. The Variety of Lines on a Cubic Fourfold
- 17. The Incidence Correspondence $I$
- 18. The Rational Self-Map $\varphi : F \dashrightarrow F$
- 19. The Fourier Decomposition for $F$
- 20. A First Multiplicative Result
- 21. The Rational Self-Map $\varphi :F\dashrightarrow F$ and the Fourier Decomposition
- 22. The Fourier Decomposition for $F$ is Multiplicative
- A. Some Geometry of Cubic Fourfolds
- B. Rational Maps and Chow Groups
Abstract
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