Memoirs of the American Mathematical Society 1995; 133 pp; softcover Volume: 116 ISBN10: 0821803417 ISBN13: 9780821803417 List Price: US$45 Individual Members: US$27 Institutional Members: US$36 Order Code: MEMO/116/557
 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, Kodairatype 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  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
