Abstract: The main contents of this volume are concentrated around V. V. Shokurov's paper Prelimiting Flips, in which the author obtained a new profound result on the existence of a 4-fold log flip. This result completes the Minimal Model Program of Mori in dimension four. The paper also presents a new simple proof of the existence of a 3-fold log flip, and an inductive approach to the existence of a log flip in any dimension. In addition, it introduces new concepts and methods of birational geometry: b-divisors, functional algebras, and saturated linear systems. Other papers of this volume are dedicated to the development of separate sections of the aforementioned paper and to the solution of certain problems stated in it.
The volume is of considerable interest to specialists in algebraic, especially birational, geometry. It is also of interest to algebraists involved in commutative graded algebras. The contents of this volume are comprehensible to mathematicians that are familiar with the fundamentals of algebraic geometry and to postgraduates of relevant specialties.
Birational Geometry: Linear Systems and Finitely Generated Algebras
Collected papers. Edited by Professor V. A. Iskovskikh and Professor V. V. Shokurov
The main contents of this volume are concentrated around V. V. Shokurov's paper Prelimiting Flips, in which the author obtained a new profound result on the existence of a 4-fold log flip. This result completes the Minimal Model Program of Mori in dimension four. The paper also presents a new simple proof of the existence of a 3-fold log flip, and an inductive approach to the existence of a log flip in any dimension. In addition, it introduces new concepts and methods of birational geometry: b-divisors, functional algebras, and saturated linear systems. Other papers of this volume are dedicated to the development of separate sections of the aforementioned paper and to the solution of certain problems stated in it.
The volume is of considerable interest to specialists in algebraic, especially birational, geometry. It is also of interest to algebraists involved in commutative graded algebras. The contents of this volume are comprehensible to mathematicians that are familiar with the fundamentals of algebraic geometry and to postgraduates of relevant specialties.
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