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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Let me give a rough picture of the Fourier-Mukai transform and how it resembles the classical situation. Home Questions Tags Users Unanswered.
Spherical and Exceptional Objects 9. There are some cool theorems of Orlov, I forget the precise statements but you can probably easily find them in any of the books suggested so farwhich say that in certain cases any derived equivalence is induced by a Fourier-Mukai transform.
To purchase, visit your inn ebook provider. Note that the converse is not true: Sign up using Email and Password. In string theory, T-duality short for target space dualitywhich relates two quantum field theories or string theories with different spacetime geometries, is closely related with the Fourier-Mukai transformation, a fact that has been greatly explored recently.
big picture – Heuristic behind the Fourier-Mukai transform – MathOverflow
Subscriber Login Email Address. Derived Category and Canonical bundle II 7. I hope this gives you a better idea of what is going on, though I have to admit that I don’t know of any good heuristic idea behind, e. Pieter Belmanssection 2. I believe you do the Fourier transform 4 times to get your original function back.
Retrieved from ” https: Dmitri OrlovDerived categories of coherent sheaves and equivalences between themRussian Math. Daniel HuybrechtsFourier-Mukai transformspdf.
Fourier-Mukai Transforms in Algebraic Geometry
Journal of High Energy Physics. I think this is supposed to be analogous to the statement I made about the classical Fourier transform being invertible. What is the heuristic idea behind the Fourier-Mukai transform?
Overview Description Table of Contents. First, recall the classical Fourier transform. Sign up or log in Sign up using Google. For a morphism f: I really know almost nothing about the classical Fourier transform, but one of the main points is that the Fourier transform is supposed to be an invertible operation.
Nagoya Mathematical Journal But to make all of this actually work out, we have to actually use the derived pushforward, not just the pushforward. And so we have to work with the derived categories. The Fourier-Mukai transform is a categorified integral transform roughly similar to the standard Fourier transform.
Fourier-Mukai Transforms in Algebraic Geometry – Daniel Huybrechts – Oxford University Press
The Mathematical World of Charles L. Classical, Early, and Medieval World History: Classical, Early, and Medieval Prose and Writers: Flips and Flops Moreover, could someone recommend a concise introduction to the subject?
Daniel Moskovich 13k 8 The pushforward of a coherent sheaf is not always coherent. Just a complement to the answer of Kevin Lin. Print Save Cite Email Share.
Just as CommRing behaves a lot like Set opI think there is probably some kind of general phenomenon that sheaves or vector bundles behave a lot like functions, which is what’s happening here. Hochschild cohomologycyclic cohomology. Post as a guest Name.