Recent Developments in Algebraic Geometry: To Miles Reid for his 70th Birthday

doi:10.1017/9781009180849

Written in celebration of Miles Reid's 70th birthday, this illuminating volume contains 11 papers by leading mathematicians in and around algebraic geometry, broadly related to the themes and interests of Reid's varied career. Just as in Reid's own scientific output, some of the papers give comprehensive accounts of the state of the art of foundational matters, while others give expositions of subject areas or techniques in concrete terms. Reid has been one of the major expositors of algebraic geometry and a great influence on many in this field – this book hopes to inspire a new generation of graduate students and researchers in his tradition.

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Contents

Frontmatter
pp i-iv
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Dedicaton
pp v-vi
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Contents
pp vii-viii
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Contributors
pp ix-x
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Happy Birthday
pp 1-3
- By Hamid Abban, Gavin Brown, Alexander Kasprzyk, Shigefumi Mori
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On Stable Cohomology of Central Extensions of Elementary Abelian Groups
pp 4-19
- By Fedor Bogomolov, Christian Böhning, Alena Pirutka
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On Projective 3-Folds of General Type with pg = 2
pp 20-65
- By Meng Chen, Yong Hu, Matteo Penegini
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15-Nodal Quartic Surfaces. Part I: Quintic del Pezzo Surfaces and Congruences of Lines in P3
pp 66-115
- By Igor V. Dolgachev
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Mori Flips, Cluster Algebras and Diptych Varieties Without Unprojection
pp 116-149
- By Tom Ducat
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The Mirror of the Cubic Surface
pp 150-182
- By Mark Gross, Paul Hacking, Sean Keel, Bernd Siebert
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Semi-Orthogonal Decomposition of a Derived Category of a 3-Fold With an Ordinary Double Point
pp 183-215
- By Yujiro Kawamata
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Duality and Normalization, Variations on a Theme of Serre and Reid
pp 216-252
- By János Kollár
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Rationality of Q-Fano Threefolds of Large Fano Index
pp 253-274
- By Yuri Prokhorov
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An Exceptional Locus in the Perfect Compactification of Ag
pp 275-295
- By N. I. Shepherd-Barron
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Variation of Stable Birational Types of Hypersurfaces
pp 296-313
- By Evgeny Shinder
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Triangle Varieties and Surface Decomposition of Hyper-Käahler Manifolds
pp 314-356
- By Claire Voisin
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Recent Developments in Algebraic Geometry

To Miles Reid for his 70th Birthday

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Contents

Frontmatter
pp i-iv

Dedicaton
pp v-vi

Contents
pp vii-viii

Contributors
pp ix-x

Happy Birthday
pp 1-3

On Stable Cohomology of Central Extensions of Elementary Abelian Groups
pp 4-19

On Projective 3-Folds of General Type with pg = 2
pp 20-65

15-Nodal Quartic Surfaces. Part I: Quintic del Pezzo Surfaces and Congruences of Lines in P3
pp 66-115

Mori Flips, Cluster Algebras and Diptych Varieties Without Unprojection
pp 116-149

The Mirror of the Cubic Surface
pp 150-182

Semi-Orthogonal Decomposition of a Derived Category of a 3-Fold With an Ordinary Double Point
pp 183-215

Duality and Normalization, Variations on a Theme of Serre and Reid
pp 216-252

Rationality of Q-Fano Threefolds of Large Fano Index
pp 253-274

An Exceptional Locus in the Perfect Compactification of Ag
pp 275-295

Variation of Stable Birational Types of Hypersurfaces
pp 296-313

Triangle Varieties and Surface Decomposition of Hyper-Käahler Manifolds
pp 314-356

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Recent Developments in Algebraic Geometry

To Miles Reid for his 70th Birthday

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