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Weyl Groups and Birational Transformations among Minimal Models
 
Kenji Matsuki Brandeis University
Weyl Groups and Birational Transformations among Minimal Models
eBook 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
Weyl Groups and Birational Transformations among Minimal Models
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Weyl Groups and Birational Transformations among Minimal Models
Kenji Matsuki Brandeis University
eBook 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
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1161995; 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1161995; 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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