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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 Click above image for expanded view 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
• 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.

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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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.