Singularities Of The Minimal Model Program
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Singularities Of The Minimal Model Program
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Author : János Kollár
language : en
Publisher: Cambridge University Press
Release Date : 2013-02-21
Singularities Of The Minimal Model Program written by János Kollár and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-21 with Mathematics categories.
An authoritative reference and the first comprehensive treatment of the singularities of the minimal model program.
Singularities Of The Minimal Model Program
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Author : János Kollár
language : en
Publisher: Cambridge University Press
Release Date : 2013-02-21
Singularities Of The Minimal Model Program written by János Kollár and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-21 with Mathematics categories.
This book gives a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties. The study of these singularities and the development of Mori's program have been deeply intertwined. Early work on minimal models relied on detailed study of terminal and canonical singularities but many later results on log terminal singularities were obtained as consequences of the minimal model program. Recent work on the abundance conjecture and on moduli of varieties of general type relies on subtle properties of log canonical singularities and conversely, the sharpest theorems about these singularities use newly developed special cases of the abundance problem. This book untangles these interwoven threads, presenting a self-contained and complete theory of these singularities, including many previously unpublished results.
Singularities Of The Minimal Model Program
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Author : János Kollár. Sándor Kovács
language : en
Publisher:
Release Date : 2013
Singularities Of The Minimal Model Program written by János Kollár. Sándor Kovács and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Introduction To The Mori Program
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Author : Kenji Matsuki
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Introduction To The Mori Program written by Kenji Matsuki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
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.
Birational Geometry Of Algebraic Varieties
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Author : Janos Kollár
language : en
Publisher: Cambridge University Press
Release Date : 2008-02-04
Birational Geometry Of Algebraic Varieties written by Janos Kollár and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-04 with Mathematics categories.
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.
Toric Varieties
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Author : David A. Cox
language : en
Publisher: American Mathematical Society
Release Date : 2024-06-25
Toric Varieties written by David A. Cox and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-25 with Mathematics categories.
Toric varieties form a beautiful and accessible part of modern algebraic geometry. This book covers the standard topics in toric geometry; a novel feature is that each of the first nine chapters contains an introductory section on the necessary background material in algebraic geometry. Other topics covered include quotient constructions, vanishing theorems, equivariant cohomology, GIT quotients, the secondary fan, and the minimal model program for toric varieties. The subject lends itself to rich examples reflected in the 134 illustrations included in the text. The book also explores connections with commutative algebra and polyhedral geometry, treating both polytopes and their unbounded cousins, polyhedra. There are appendices on the history of toric varieties and the computational tools available to investigate nontrivial examples in toric geometry. Readers of this book should be familiar with the material covered in basic graduate courses in algebra and topology, and to a somewhat lesser degree, complex analysis. In addition, the authors assume that the reader has had some previous experience with algebraic geometry at an advanced undergraduate level. The book will be a useful reference for graduate students and researchers who are interested in algebraic geometry, polyhedral geometry, and toric varieties.
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes
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Author : Boyan Sirakov
language : en
Publisher: World Scientific
Release Date : 2019-02-27
Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes written by Boyan Sirakov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-27 with Mathematics categories.
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Handbook Of Geometry And Topology Of Singularities Iv
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Author : José Luis Cisneros-Molina
language : en
Publisher: Springer Nature
Release Date : 2023-10-07
Handbook Of Geometry And Topology Of Singularities Iv written by José Luis Cisneros-Molina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-07 with Mathematics categories.
This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, the Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex. Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
Snowbird Lectures In Algebraic Geometry
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Author : Ravi Vakil
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Snowbird Lectures In Algebraic Geometry written by Ravi Vakil and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
A significant part of the 2004 Summer Research Conference on Algebraic Geometry (Snowbird, UT) was devoted to lectures introducing the participants, in particular, graduate students and recent Ph.D.'s, to a wide swathe of algebraic geometry and giving them a working familiarity with exciting, rapidly developing parts of the field. One of the main goals of the organizers was to allow the participants to broaden their horizons beyond the narrow area in which they are working. A fine selection of topics and a noteworthy list of contributors made the resulting collection of articles a useful resource for everyone interested in getting acquainted with the modern topic of algebraic geometry. The book consists of ten articles covering, among others, the following topics: the minimal model program, derived categories of sheaves on algebraic varieties, Kobayashi hyperbolicity, groupoids and quotients in algebraic geometry, rigid analytic varieties, and equivariant cohomology. Suitable for independent study, this unique volume is intended for graduate students and researchers interested in algebraic geometry.
Topology Of Stratified Spaces
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Author : Greg Friedman
language : en
Publisher: Cambridge University Press
Release Date : 2011-03-28
Topology Of Stratified Spaces written by Greg Friedman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-28 with Mathematics categories.
This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.