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Recent developments in algebraic geometry : to Miles Reid for his 70th birthday / edited by Hamid Abban, Loughborough University ; Gavin Brown, University of Warwick ; Alexander Kasprzyk, University of Nottingham ; Shigefumi Mori, Kyoto University.

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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 paper...

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Bibliographic Details
Online Access: Full Text (via ProQuest)
Main Authors: Abban, Hamid, 1983- (Author), Brown, Gavin, 1968- (Author), Kasprzyk, Alexander, 1980- (Author), Mori, Shigefumi (Author)
Format: eBook
Language:English
Published: Cambridge, United Kingdom ; New York, NY, USA : Cambridge University Press, 2022.
Series:London Mathematical Society lecture note series ; 478.
Subjects:
Reid, Miles > (Miles A.) > Influence.
Geometry, Algebraic.
Geometry, Algebraic
Influence (Literary, artistic, etc.)
Table of Contents:
  • Cover
  • Series page
  • Title page
  • Copyright page
  • Dedication
  • Contents
  • List of Contributors
  • Happy Birthday
  • References
  • On Stable Cohomology of Central Extensions of Elementary Abelian Groups
  • Abstract
  • 1 Introduction and Statement of Results
  • 2 Some Linear Algebra
  • 3 Proofs of Main Results
  • Acknowledgements
  • References
  • On Projective 3-Folds of General Type with p[sub(g)] = 2
  • Abstract
  • 1 Introduction
  • 2 Preliminaries
  • 2.1 Set Up
  • 2.2 Convention
  • 2.3 Known Inequalities
  • 2.4 Birationality Principle
  • 2.5 A Weak Form of Extension Theorem
  • 2.6 The Weighted Basket of X
  • 3 Some Technical Theorems
  • 3.1 Two Restriction Maps on Canonical Class of (1, 2)-Surfaces
  • 4 Threefolds of General Type with p[sub(g)] = 2
  • 4.1 Non-(1, 2)-Surface Case
  • 4.2 The (1, 2)-Surface Case
  • 4.3 Effective Constraints on P[sub(2)], P[sub(3)], P[sub(4)], P[sub(5)] and P[sub(6)]
  • 4.4 Estimation of the Canonical Volume
  • 4.5 The Classification of B[sup((5))](X)
  • Acknowledgements
  • References
  • 15-Nodal Quartic Surfaces. Part I: Quintic del Pezzo Surfaces and Congruences of Lines in P[sup(3)]
  • Abstract
  • 1 Introduction
  • 2 Generalities on Congruences of Lines
  • 2.1
  • 2.2
  • 2.3
  • 3 Congruences of Degree 2 and Class n
  • 3.1
  • 3.2
  • 4 Congruences of Bidegree (2, 3)
  • 4.1
  • 4.2
  • 4.3
  • 5 The Segre Cubic and Castelnuovo-Richmond-Igusa Quartic
  • 5.1
  • 5.2
  • 5.3
  • 6 15-Nodal Quartic Surfaces
  • 6.1
  • 6.2
  • 6.3
  • 6.4
  • 6.5
  • 7 Degree 10 Model of a 15-Nodal Quartic Surface
  • 7.1
  • 7.2
  • 7.3
  • 7.4
  • 8 The Picard Group
  • 8.1
  • 8.2
  • 9 Admissible Pentads
  • 9.1
  • 9.2
  • References
  • Mori Flips, Cluster Algebras and Diptych Varieties Without Unprojection
  • Abstract
  • 1 Introduction
  • 2 Mori Flips
  • 2.1 Extremal Neighbourhoods
  • 2.2 The Affine Cover of an Extremal Neighbourhood
  • 2.3 Type A Flips
  • 3 Cluster Algebras
  • 3.1 The Cluster Algebra A
  • 3.2 The Upper Cluster Algebra U
  • 3.3 Expanding in a Cluster
  • 4 Mori's Algorithm
  • 4.1 Local Model of a k2A Neighbourhood
  • 4.2 Mori's Continued Division Algorithm
  • 4.3 Describing the Flip
  • 4.4 Key Varieties for Mori Flips
  • 5 Diptych Varieties
  • 5.1 Smoothing a Tent
  • 5.2 Classification of Diptych Varieties
  • 6 Proof of Theorem 1.1
  • 6.1 Diptych Varieties as Cluster Varieties

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