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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Thanks, that looks very interesting.
You may want to look at Tom Bridgeland’s PhD thesis. It interchanges Pontrjagin product and tensor product.
The following answers might be useful: Hence this is a pull-tensor-push integral transform through the product correspondence. That equivalence is analogous to the classical Fourier transform fouriee gives an isomorphism between tempered distributions on a finite-dimensional real vector space and its dual. Classical, Early, and Medieval World History: The pushforward of a coherent sheaf is not always coherent.
Remark It was believed that theorem should be true for all triangulated functors e. I tend to disagree, you write: Discussion of internal homs of dg-categories in terms of refined Fourier-Mukai transforms is in.
The final chapter summarizes recent research directions, such as connections to orbifolds and the representation theory of finite groups via the McKay correspondence, stability conditions on triangulated categories, and the notion of the derived category of sheaves twisted by a gerbe. GMRA 1, 2 23 To purchase, visit your preferred ebook provider. The real reason to use derived category is that there are higher direct images.
Fourier-Mukai Transforms in Algebraic Geometry
Ebook This title is available as an ebook. Aimed at postgraduate students with a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety.
This page was last edited on 20 Septemberat Most natural functors, including basic ones like pushforwards and pullbacksare of this type. The Fourier-Mukai transform is a categorified integral transform roughly similar to the standard Fourier transform.
It was believed that theorem should be true for all triangulated functors e.
big picture – Heuristic behind the Fourier-Mukai transform – MathOverflow
Advances in Theoretical and Mathematical Physics. Where to Go from Here References Index. I think this was proven by Mukai. 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. This also happens to be one of my favourite books.
The derived category is a subtle invariant of the isomorphism type of a variety, and its group of autoequivalences often shows a rich structure. But there is certainly something deep going on.
Fourier-Mukai Transforms in Algebraic Geometry – Daniel Huybrechts – Oxford University Press
I believe you do the Fourier transform 4 times to get your original function back.