This seminal text on Fourier-Mukai Transforms in Algebraic Geometry by a leading researcher and expositor is based on a course given at the. Fourier-Mukai transforms in algebraic geometry. CHTS. Mathematisches Institut Universitat Bonn. CLARENDON PRESS • OXFORD. In algebraic geometry, a Fourier–Mukai transform ΦK is a functor between derived categories of coherent sheaves D(X) → D(Y) for schemes X and Y, which is.
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The derived category is a subtle invariant of the isomorphism type of a variety, and its group of autoequivalences often shows a rich structure.
The Fourier-Mukai transfofms in algebraic geometry gets its name because it at least superficially resembles the classical Fourier transform. Fourier-Mukai transform – a first example Intuition for Integral Transforms Fourier transform for dummies The last one has my sketch of an answer which I’ll post here once it gets better. And of course because it mjkai studied by Mukai. As it turns out — and this feature mukwi pursued throughout the book — the behaviour of the derived category is determined by the geometric properties of the canonical bundle of the variety.
Lin Dec 27 ’09 at Views Read Edit View history.
In particular, without derived category the base change would not algebdaic, so you cannot prove anything about F-M transform e. The final chapter summarizes recent research directions, such as connections to orbifolds and the representation theory of finite groups geometyr the McKay correspondence, stability conditions on triangulated categories, and the notion of the derived category of sheaves twisted by a gerbe.
Just a complement to the answer of Kevin Lin. Generally, for XY X,Y two suitably well-behaved schemes e. Let g denote the dimension of X.
Flips and Flops Academic Skip to main content. Authors Affiliations are at time of print publication. BenZvi-Nadler-Preygel 13 and lots of other contexts.
Post as a guest Name. This dictionnary was one of the motivation for the formulation of the geometric Langlands program see some expository articles of Frenkel for example. But there is certainly something deep going on. Thanks, that looks very interesting.
A Clarendon Press Publication. Dmitri OrlovDerived categories of coherent sheaves and algberaic between themRussian Math. It’s something like this: Aimed at postgraduate students with a geomftry knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. What is the connection to the classical Fourier transform?
It exists, it is the Fourier-Deligne transform. GMRA 1, 2 23 The Fourier—Mukai transformation is nearly involutive:. Pieter Belmanssection 2.
big picture – Heuristic behind the Fourier-Mukai transform – MathOverflow
Nagoya Mathematical Journal However according to RVdB this is geimetry true. This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view.