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Fourier-Mukai transforms in algebraic geometry /
This work is based on a course given at the Institut de Mathematiques de Jussieu, on the derived category of coherent sheaves on a smooth projective variety. It is aimed at students with a basic knowledge of algebraic geometry and contains full proofs and exercises that aid the reader.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford :
Clarendon Press,
2006.
|
| Colección: | Oxford mathematical monographs.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Huybrechts, Daniel, |e author. | |
| 245 | 1 | 0 | |a Fourier-Mukai transforms in algebraic geometry / |c D. Huybrechts. |
| 260 | |a Oxford : |b Clarendon Press, |c 2006. | ||
| 300 | |a 1 online resource (viii, 307 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file | ||
| 380 | |a Bibliography | ||
| 490 | 1 | |a Oxford mathematical monographs | |
| 504 | |a Includes bibliographical references and index. | ||
| 520 | 8 | |a This work is based on a course given at the Institut de Mathematiques de Jussieu, on the derived category of coherent sheaves on a smooth projective variety. It is aimed at students with a basic knowledge of algebraic geometry and contains full proofs and exercises that aid the reader. | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Contents -- 1 Triangulated categories -- 1.1 Additive categories and functors -- 1.2 Triangulated categories and exact functors -- 1.3 Equivalences of triangulated categories -- 1.4 Exceptional sequences and orthogonal decompositions -- 2 Derived categories: a quick tour -- 2.1 Derived category of an abelian category -- 2.2 Derived functors -- 2.3 Spectral sequences -- 3 Derived categories of coherent sheaves -- 3.1 Basic structure -- 3.2 Spanning classes in the derived category -- 3.3 Derived functors in algebraic geometry -- 3.4 Grothendieck�Verdier duality | |
| 505 | 8 | |a 4 Derived category and canonical bundle � I4.1 Ample (anti- )canonical bundle -- 4.2 Autoequivalences for ample (anti- )canonical bundle -- 4.3 Ample sequences in derived categories -- 5 Fourier�Mukai transforms -- 5.1 What it is and Orlov�s result -- 5.2 Passage to cohomology -- 6 Derived category and canonical bundle � II -- 6.1 Kodaira dimension under derived equivalence -- 6.2 Geometrical aspects of the Fourier�Mukai kernel -- 6.3 Nefness under derived equivalence -- 6.4 Derived equivalence versus birationality | |
| 505 | 8 | |a 6.5 Recap: Kodaira dimension, canonical ring, etc. 7 Equivalence criteria for Fourier�Mukai transforms -- 7.1 Fully faithful -- 7.2 Equivalences -- 7.3 Canonical quotients -- 8 Spherical and exceptional objects -- 8.1 Autoequivalences induced by spherical objects -- 8.2 Braid group actions -- 8.3 Beilinson spectral sequence -- 8.4 They go together -- 9 Abelian varieties -- 9.1 Basic definitions and facts -- 9.2 The Poincaré bundle as a Fourier�Mukai kernel -- 9.3 Sl[Sub(2)]-action -- 9.4 Derived equivalences of abelian varieties | |
| 505 | 8 | |a ""9.5 Autoequivalences of abelian varieties""""10 K3 surfaces""; ""10.1 Recap: K3 surfaces""; ""10.2 Derived equivalence of K3 surfaces""; ""10.3 Recap: Moduli spaces of sheaves""; ""11 Flips and flops""; ""11.1 Preparations: Closed embeddings and blow-ups""; ""11.2 Derived categories under blow-up""; ""11.3 The standard flip""; ""11.4 The Mukai flop""; ""12 Derived categories of surfaces""; ""12.1 Recap: Enriques classification of algebraic surfaces""; ""12.2 Minimal surfaces with kod = â€?∞, 2""; ""12.3 Surfaces with torsion canonical bundle""; ""12.4 Properly elliptic surfaces"" | |
| 505 | 8 | |a 13 Where to go from here13.1 McKay correspondence for derived categories -- 13.2 Homological mirror symmetry -- 13.3 D-branes and stability conditions -- 13.4 Twisted derived categories -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- O -- P -- Q -- R -- S -- T -- Y | |
| 546 | |a English. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Fourier transformations. | |
| 650 | 0 | |a Geometry, Algebraic. | |
| 650 | 6 | |a Géométrie algébrique. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Algebraic. |2 bisacsh | |
| 650 | 7 | |a Fourier transformations |2 fast | |
| 650 | 7 | |a Geometry, Algebraic |2 fast | |
| 758 | |i has work: |a Fourier-Mukai transforms in algebraic geometry (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFGkKPkQ3xdjMpRHTkqYj3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Huybrechts, Daniel. |t Fourier-Mukai transforms in algebraic geometry. |d Oxford : Clarendon Press, 2006 |z 0199296863 |z 9780199296866 |w (DLC) 2006298244 |w (OCoLC)64097295 |
| 830 | 0 | |a Oxford mathematical monographs. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=3052126 |z Texto completo |
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