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Weyl Groups and Birational Transformations among Minimal Models
 
Kenji Matsuki :  Brandeis University
Front Cover for Weyl Groups and Birational Transformations among Minimal Models
Available Formats:
Electronic ISBN: 978-1-4704-0136-8
Product Code: MEMO/116/557.E
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $27.00
Add to cart
Front Cover for Weyl Groups and Birational Transformations among Minimal Models
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  • Front Cover for Weyl Groups and Birational Transformations among Minimal Models
  • Back Cover for Weyl Groups and Birational Transformations among Minimal Models
Weyl Groups and Birational Transformations among Minimal Models
Kenji Matsuki :  Brandeis University
Available Formats:
Electronic ISBN:  978-1-4704-0136-8
Product Code:  MEMO/116/557.E
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $27.00
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 116; 1995; 133 pp
    MSC: Primary 14;

    This work provides a unified way of looking at the apparently sporadic Weyl groups connected with the classical algebraic geometry of surfaces from the viewpoint of the recently established Minimal Model Program for \(3\)-folds (Mori's Program). Matsuki explores the correspondence between the algebraic objects (the Weyl chambers, roots, reflections) and geometric objects (the ample cones of minimal models, extremal rays, flops) for the Weyl groups appearing with rational double points, Kodaira-type degenerations of elliptic curves and K3 surfaces. A complete table for all the extremal rays of Fano \(3\)-folds also appears here for the first time, along with some interesting examples of flops for \(4\)-folds.
    Readership

    Research mathematicians, researchers in algebraic geometry.
  • Table of Contents
     
     
    • Chapters
    • I. Introduction
    • II. Weyl groups appearing in the symmetry among minimal models
    • III. Weyl groups for Fano 3-folds
    • IV. Summary and speculation about the connection with algebraic groups
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Memoirs of the American Mathematical Society
Volume: 116; 1995; 133 pp
MSC: Primary 14;

This work provides a unified way of looking at the apparently sporadic Weyl groups connected with the classical algebraic geometry of surfaces from the viewpoint of the recently established Minimal Model Program for \(3\)-folds (Mori's Program). Matsuki explores the correspondence between the algebraic objects (the Weyl chambers, roots, reflections) and geometric objects (the ample cones of minimal models, extremal rays, flops) for the Weyl groups appearing with rational double points, Kodaira-type degenerations of elliptic curves and K3 surfaces. A complete table for all the extremal rays of Fano \(3\)-folds also appears here for the first time, along with some interesting examples of flops for \(4\)-folds.
Readership

Research mathematicians, researchers in algebraic geometry.
  • Chapters
  • I. Introduction
  • II. Weyl groups appearing in the symmetry among minimal models
  • III. Weyl groups for Fano 3-folds
  • IV. Summary and speculation about the connection with algebraic groups
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