Weyl groups and birational transformations among minimal models / Kenji Matsuki.

Format:

Book

Author/Creator:

Matsuki, Kenji, 1958- author.

Series:

Memoirs of the American Mathematical Society ; Number 557.

Memoirs of the American Mathematical Society, 0065-9266 ; Number 557

Language:

English

Subjects (All):

Surfaces, Algebraic.

Weyl groups.

Threefolds (Algebraic geometry).

Physical Description:

1 online resource (146 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1995.

Language Note:

English

Summary:

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.

Contents:

""Contents""; ""Chapter I. Introduction""; ""Chapter II. Weyl groups appearing in the symmetry among minimal models""; ""ÂII-1. 3â€?folds of general type â€? Weyl groups of finite type""; ""ÂII-1-1. The case of rational double points""; ""ÂII-1-2. The case of Del Pezzo surfaces""; ""ÂII-1-3. The case of ruled surfaces""; ""ÂII-2. Elliptic 3-folds â€? Weyl groups of affine type""; ""ÂII-2-1. The case of Kodairaâ€?type degenerations of elliptic curves""; ""ÂII-3. 3â€?folds with Kodaira dimension 1 â€? Weyl groups of hyperbolic type""

""ÂII-3-1. The case of Picardâ€?Lefschetz reflections of K3 surfaces""""ÂII-4. 3-folds with Kodaira dimension 0""; ""ÂII-4-1. The case of generic quintic 3â€?folds""; ""Chapter III. Weyl groups for Fano 3â€?folds""; ""ÂIII-1. Characterization of the Weyl groups for Del Pezzo surfaces and its generalization to Fano manifolds of higher dimensions""; ""ÂIII-2. Flops in dimension 4""; ""ÂIII-3. Table for the Weyl groups for Fano 3â€?folds""; ""Chapter IV. Summary and speculation about the connection with algebraic groups""; ""References""

Notes:

"July 1995, Volume 116, Number 557 (end of volume)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0136-3