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Introduction to the Mori Program

Introduction to the Mori Program
Author: Kenji Matsuki
Publisher: Springer Science & Business Media
Total Pages: 502
Release: 2013-04-17
Genre: Mathematics
ISBN: 147575602X

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Mori's Program is a fusion of the so-called Minimal Model Program and the IItaka Program toward the biregular and/or birational classification of higher dimensional algebraic varieties. The author presents this theory in an easy and understandable way with lots of background motivation. Prerequisites are those covered in Hartshorne's book "Algebraic Geometry." This is the first book in this extremely important and active field of research and will become a key resource for graduate students wanting to get into the area.


Singularities of the Minimal Model Program

Singularities of the Minimal Model Program
Author: János Kollár
Publisher: Cambridge University Press
Total Pages: 381
Release: 2013-02-21
Genre: Mathematics
ISBN: 1107035341

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An authoritative reference and the first comprehensive treatment of the singularities of the minimal model program.


Foundations of the minimal model program

Foundations of the minimal model program
Author: 藤野修 (代数学)
Publisher: Mathematical Society of Japan Memoirs
Total Pages: 0
Release: 2017-05
Genre: Geometry, Algebraic
ISBN: 9784864970457

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Around 1980, Shigefumi Mori initiated a new theory, which is now known as the minimal model program or Mori theory, for higher-dimensional algebraic varieties. This theory has developed into a powerful tool with applications to diverse questions in algebraic geometry and related fields.One of the main purposes of this book is to establish the fundamental theorems of the minimal model program, that is, various Kodaira type vanishing theorems, the cone and contraction theorem, and so on, for quasi-log schemes. The notion of quasi-log schemes was introduced by Florin Ambro and is now indispensable for the study of semi-log canonical pairs from the cohomological point of view. By the recent developments of the minimal model program, we know that the appropriate singularities to permit on the varieties at the boundaries of moduli spaces are semi-log canonical. In order to achieve this goal, we generalize Kollár's injectivity, torsion-free, and vanishing theorems for reducible varieties by using the theory of mixed Hodge structures on cohomology with compact support. We also review many important classical Kodaira type vanishing theorems in detail and explain the basic results of the minimal model program for the reader's convenience.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets


Birational Geometry of Algebraic Varieties

Birational Geometry of Algebraic Varieties
Author: Janos Kollár
Publisher: Cambridge University Press
Total Pages: 264
Release: 2008-02-04
Genre: Mathematics
ISBN: 9780521060226

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One of the major discoveries of the past two decades in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program, or Mori's program, has developed into a powerful tool with applications to diverse questions in algebraic geometry and beyond. This book provides the first comprehensive introduction to the circle of ideas developed around the program, the prerequisites being only a basic knowledge of algebraic geometry. It will be of great interest to graduate students and researchers working in algebraic geometry and related fields.


Tuesdays with Morrie

Tuesdays with Morrie
Author: Mitch Albom
Publisher: Crown
Total Pages: 226
Release: 2007-06-29
Genre: Biography & Autobiography
ISBN: 0307414094

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#1 NEW YORK TIMES BESTSELLER • A special 25th anniversary edition of the beloved book that has changed millions of lives with the story of an unforgettable friendship, the timeless wisdom of older generations, and healing lessons on loss and grief—featuring a new afterword by the author “A wonderful book, a story of the heart told by a writer with soul.”—Los Angeles Times “The most important thing in life is to learn how to give out love, and to let it come in.” Maybe it was a grandparent, or a teacher, or a colleague. Someone older, patient and wise, who understood you when you were young and searching, helped you see the world as a more profound place, gave you sound advice to help you make your way through it. For Mitch Albom, that person was his college professor Morrie Schwartz. Maybe, like Mitch, you lost track of this mentor as you made your way, and the insights faded, and the world seemed colder. Wouldn’t you like to see that person again, ask the bigger questions that still haunt you, receive wisdom for your busy life today the way you once did when you were younger? Mitch Albom had that second chance. He rediscovered Morrie in the last months of the older man’s life. Knowing he was dying, Morrie visited with Mitch in his study every Tuesday, just as they used to back in college. Their rekindled relationship turned into one final “class”: lessons in how to live. “The truth is, Mitch,” he said, “once you learn how to die, you learn how to live.” Tuesdays with Morrie is a magical chronicle of their time together, through which Mitch shares Morrie’s lasting gift with the world.


Understanding and Using Linear Programming

Understanding and Using Linear Programming
Author: Jiri Matousek
Publisher: Springer Science & Business Media
Total Pages: 230
Release: 2007-07-04
Genre: Mathematics
ISBN: 3540307176

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The book is an introductory textbook mainly for students of computer science and mathematics. Our guiding phrase is "what every theoretical computer scientist should know about linear programming". A major focus is on applications of linear programming, both in practice and in theory. The book is concise, but at the same time, the main results are covered with complete proofs and in sufficient detail, ready for presentation in class. The book does not require more prerequisites than basic linear algebra, which is summarized in an appendix. One of its main goals is to help the reader to see linear programming "behind the scenes".


An Introduction to Ordinary Differential Equations

An Introduction to Ordinary Differential Equations
Author: Ravi P. Agarwal
Publisher: Springer Science & Business Media
Total Pages: 333
Release: 2008-12-10
Genre: Mathematics
ISBN: 0387712763

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Ordinary differential equations serve as mathematical models for many exciting real world problems. Rapid growth in the theory and applications of differential equations has resulted in a continued interest in their study by students in many disciplines. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures that effectively convey the subject in easily manageable sections. The presentation is driven by detailed examples that illustrate how the subject works. Numerous exercise sets, with an "answers and hints" section, are included. The book further provides a background and history of the subject.


An Introduction to Sequential Dynamical Systems

An Introduction to Sequential Dynamical Systems
Author: Henning Mortveit
Publisher: Springer Science & Business Media
Total Pages: 261
Release: 2007-11-27
Genre: Mathematics
ISBN: 0387498796

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This introductory text to the class of Sequential Dynamical Systems (SDS) is the first textbook on this timely subject. Driven by numerous examples and thought-provoking problems throughout, the presentation offers good foundational material on finite discrete dynamical systems, which then leads systematically to an introduction of SDS. From a broad range of topics on structure theory - equivalence, fixed points, invertibility and other phase space properties - thereafter SDS relations to graph theory, classical dynamical systems as well as SDS applications in computer science are explored. This is a versatile interdisciplinary textbook.


Death in Documentaries

Death in Documentaries
Author: Benjamin Bennett-Carpenter
Publisher: BRILL
Total Pages: 232
Release: 2017-11-13
Genre: Philosophy
ISBN: 9004356967

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In Death in Documentaries: The Memento Mori Experience, Benjamin Bennett-Carpenter suggests that documentaries are an especially apt form of contemporary memento mori; that is, documentaries offer transformative experiences for a viewer to renew one’s consciousness of mortality.


Algebraic Geometry

Algebraic Geometry
Author: Robin Hartshorne
Publisher: Springer Science & Business Media
Total Pages: 511
Release: 2013-06-29
Genre: Mathematics
ISBN: 1475738498

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An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.