Software

FOURIER MUKAI TRANSFORMS IN ALGEBRAIC GEOMETRY PDF

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.

Author: Malakinos Shanos
Country: Saudi Arabia
Language: English (Spanish)
Genre: Health and Food
Published (Last): 15 July 2015
Pages: 330
PDF File Size: 11.47 Mb
ePub File Size: 11.19 Mb
ISBN: 117-9-23257-582-7
Downloads: 81552
Price: Free* [*Free Regsitration Required]
Uploader: Shaktizshura

Surveys, 583,translation.

Flips and Flops There is a case where the analogy between sheaves and functions is more than analogy: Most natural functors, including basic ones geomegry pushforwards and pullbacksare of this type. This site is running on Instiki 0. The derived category is a subtle invariant of the isomorphism type of a variety, and its group of autoequivalences often shows a rich structure. 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.

Fourier–Mukai transform

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 gepmetry greatly explored recently. It interchanges Pontrjagin product and tensor product.

As it turns out — and this feature algebbraic pursued throughout the book — the behaviour of the derived category is determined by the geometric properties of the canonical bundle of the variety.

  D2K INTERVIEW QUESTIONS AND ANSWERS PDF

Assuming a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. Ilya Nikokoshev 8, 9 60 Fourier-Mukai transforms always have left and right adjointsboth of which are also kernel transformations.

Hence this is a pull-tensor-push integral transform through the product correspondence. Tensor product of sheaves behave a lot like multiplication of functions Front Matter Title Pages Preface. This seminal text on Fourier-Mukai Transforms in Algebraic Geometry by a leading researcher and expositor is based on a geonetry given at the Institut de Mathematiques de Jussieu in and Sign up using Email and Password.

Alexei BondalMichel van den Bergh. A Quick Tour 3.

Fourier-Mukai Transforms in Algebraic Geometry – Oxford Scholarship

Generally, for XY X,Y two suitably well-behaved schemes e. 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. Including notions from other areas, e. More This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view.

Ebook This title is available as an ebook. Introduction to Basic Homotopy Theory. And so we have to work with the derived categories. I second Kevin’s suggestion of Huybrechts’ book, but if you want to to look at something shorter first I recommend the notes by Hille and van den Bergh. Huybrechts Abstract This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view.

  CATALOGO POLIFORM PDF

Derived Category and Canonical bundle II 7. Don’t have an account? Equivalence Criteria for Fourier-Mukai Transforms 8. This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. First, recall the classical Fourier transform.

Fourier–Mukai transform – Wikipedia

Views Read Edit View history. Pullback of sheaves behave a lot like pullback of functions 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.

Pieter Belmanssection 2. The real reason to use derived category is that there are higher direct images. Hodge theoryHodge theorem. I tend to disagree, you write: In particular, without derived category the base change would not work, so you cannot prove anything about F-M transform e.

The Mathematical World of Charles L. Overview Description Table of Contents. Classical, Early, and Medieval Prose and Writers: Spherical and Exceptional Objects 9.

Let g denote the dimension of X. Advances in Theoretical and Mathematical Physics. Note that the converse is not true: Introduction to Abstract Homotopy Theory.