Fourier-Mukai Transforms in Algebraic Geometry

Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics
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  • Academy of Europe: Publications
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  • D. Huybrechts
  • Fourier-Mukai transforms in algebraic geometry
  • Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics

    • Distinguished triangles. The homotopy category is triangulated.

    Alexander Kuznetsov : Geometry and moduli spaces of Gushel-Mukai varieties

    Lecture 4: Cohomological functors. Localization of categories. Localizing classes of morphisms. Roofs and equivalence classes of roots.

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    Lecture 5: Quasi-isomorphisms form a localizing family in the homotopy category. Localizations of additive categories are additive. Lecture 6: Localizations of abelian categories are abelian. Classes of morphisms compatible with the triangulated structure. Localization of triangulated categories.

    Short exact sequences of complexes induce distinguished triangles in the derived category. Lecture 7: Variations of the derived category: relative categories, bounded derived categoriy. Criteria for obtaining full subcategories. Truncation functors. Derived functors. The case of exact functors. Injective and projective objects. Strategy for the construction of derived functors.

    Academy of Europe: Publications

    Lecture 8: Homotopy category for complexes of injectives. Abelian categories with enough injectives, and their derived categories compared to the homotopy category of injectives. Lecture 9: Ext's and the derived category. Adapted objects. Examples: injectives are adapted for all functors, flabby and soft sheaves.

    Abstract de Rham theorem. Lecture More on the derived category of coherent sheaves and quasicoherent sheaves.

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    Composition of functors. Spectral sequences. Lecture Double complexes.

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    Horseshoe lemma. Description Table of Contents Product Details Click on the cover image above to read some pages of this book! Industry Reviews From the reviews: "The main aim of the book under review is to study a class of functors between derived categories of coherent sheaves of smooth varieties, known as integral or, in some cases, Fourier-Mukai functors. Preface p. All Rights Reserved.

    Practical information

    More Books in Physics See All. Tome 28 , pp. Principal bundles on elliptic fibrations , Asian J. Flatness and privilege , Enseignement Math. New appendix and translation from the second German edition by R. Schwarzenberger, with an additional section by A.

    D. Huybrechts

    Heuristic behind the Fourier-Mukai transform Ask Question. Let me give a rough picture of the Fourier-Mukai transform and how it resembles the classical situation. Schneider, H. Evans, Syzygies, L. Bondal, D.

    Kyoto Univ. Free download.

    Fourier-Mukai transforms in algebraic geometry

    D. Huybrechts. This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth. a Fourier-Mukai transform between the derived categories of two abelian varieties. spread as mine, and in particular study algebraic geometry, which again is.

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    • Analysis and Mechanics. Fourth International Conference on Fracture June 1977 University of Waterloo, Canada.
    • The Barbarian Principle: Merleau-Ponty, Schelling, and the Question of Nature (SUNY Series in Contemporary Continental Philosophy).
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    This seminal text by a leading researcher is based on a course given at the Institut de Mathematiques de Jussieu. Aimed at 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.

    Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics

    Full proofs are given and exercises aid the reader throughout. Passar bra ihop.

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