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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 mathrm{CH}^*(A). By using a codimension-2 algebraic cycle representing the Beauvilleâe"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.

Fourier transformations. --- Kählerian manifolds.

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Fourier transformations. --- Kählerian manifolds. --- Transformations de Fourier --- Variétés kählériennes --- Fourier transformations --- Kählerian manifolds --- Kählerian manifolds. --- Variétés kählériennes

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Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. The final part of the text studies several aspects of compact Kähler manifolds: the Calabi conjecture, Weitzenböck techniques, Calabi-Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.

Kählerian manifolds --- Variétés kählériennes --- Kählerian manifolds. --- Geometry, Algebraic. --- Algebraic geometry --- Geometry --- Geometry, Differential --- Kählerian structures --- Manifolds (Mathematics) --- Kahlerian manifolds.

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Kählerian manifolds. --- Manifolds (Mathematics) --- Invariants. --- Geometry, Differential. --- Differential geometry --- Geometry, Differential --- Topology --- Kählerian structures --- Kahlerian manifolds.

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Geometry, Differential. --- Géometrie différentielle --- Kählerian manifolds. --- Variétés kählériennes --- Geometrie differentielle locale et globale --- Geometrie differentielle locale et globale