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Weyl Groups and Birational Transformations among Minimal Models
Kenji Matsuki

Memoirs of the American Mathematical Society
1995; 133 pp; softcover
Volume: 116
ISBN-10: 0-8218-0341-7
ISBN-13: 978-0-8218-0341-7
List Price: US$45
Individual Members: US$27
Institutional Members: US$36
Order Code: MEMO/116/557
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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.


Research mathematicians, researchers in algebraic geometry.

Table of Contents

  • Introduction
  • Weyl groups appearing in the symmetry among minimal models
  • Weyl groups for Fano \(3\)-folds
  • Summary and speculation about the connection with algebraic groups
  • References
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