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Author: Masayoshi Nagata
Publisher: American Mathematical Soc.
ISBN: 9780821816875
Category : Geometry, Affine
Languages : en
Pages : 44
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Book Description
This volume contains expository lectures from the Conference Board of the Mathematical Sciences Regional Conference held at Northern Illinois University on July 25-29, 1977.
Author: Masayoshi Nagata
Publisher: American Mathematical Soc.
ISBN: 9780821816875
Category : Geometry, Affine
Languages : en
Pages : 44
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Book Description
This volume contains expository lectures from the Conference Board of the Mathematical Sciences Regional Conference held at Northern Illinois University on July 25-29, 1977.
Author: Shigeru Kuroda
Publisher: Springer Nature
ISBN: 3030421368
Category : Mathematics
Languages : en
Pages : 317
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Book Description
This proceedings volume gathers selected, peer-reviewed works presented at the Polynomial Rings and Affine Algebraic Geometry Conference, which was held at Tokyo Metropolitan University on February 12-16, 2018. Readers will find some of the latest research conducted by an international group of experts on affine and projective algebraic geometry. The topics covered include group actions and linearization, automorphism groups and their structure as infinite-dimensional varieties, invariant theory, the Cancellation Problem, the Embedding Problem, Mathieu spaces and the Jacobian Conjecture, the Dolgachev-Weisfeiler Conjecture, classification of curves and surfaces, real forms of complex varieties, and questions of rationality, unirationality, and birationality. These papers will be of interest to all researchers and graduate students working in the fields of affine and projective algebraic geometry, as well as on certain aspects of commutative algebra, Lie theory, symplectic geometry and Stein manifolds.
Author: Masayoshi Miyanishi
Publisher: World Scientific
ISBN: 981128010X
Category : Mathematics
Languages : en
Pages : 441
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Book Description
Algebraic geometry is more advanced with the completeness condition for projective or complete varieties. Many geometric properties are well described by the finiteness or the vanishing of sheaf cohomologies on such varieties. For non-complete varieties like affine algebraic varieties, sheaf cohomology does not work well and research progress used to be slow, although affine spaces and polynomial rings are fundamental building blocks of algebraic geometry. Progress was rapid since the Abhyankar-Moh-Suzuki Theorem of embedded affine line was proved, and logarithmic geometry was introduced by Iitaka and Kawamata.Readers will find the book covers vast basic material on an extremely rigorous level:
Author: Karen E. Smith
Publisher: Springer Science & Business Media
ISBN: 1475744978
Category : Mathematics
Languages : en
Pages : 173
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Book Description
This is a description of the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.
Author: David Eisenbud
Publisher: Springer Science & Business Media
ISBN: 0387226397
Category : Mathematics
Languages : en
Pages : 265
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Book Description
Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
Author: K. R. Goodearl
Publisher: Cambridge University Press
ISBN: 9780521545372
Category : Mathematics
Languages : en
Pages : 372
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Book Description
This introduction to noncommutative noetherian rings is intended to be accessible to anyone with a basic background in abstract algebra. It can be used as a second-year graduate text, or as a self-contained reference. Extensive explanatory discussion is given, and exercises are integrated throughout. This edition incorporates substantial revisions, particularly in the first third of the book, where the presentation has been changed to increase accessibility and topicality. New material includes the basic types of quantum groups, which then serve as test cases for the theory developed.
Author: Gene Freudenburg
Publisher: Springer
ISBN: 3662553503
Category : Mathematics
Languages : en
Pages : 333
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Book Description
This book explores the theory and application of locally nilpotent derivations, a subject motivated by questions in affine algebraic geometry and having fundamental connections to areas such as commutative algebra, representation theory, Lie algebras and differential equations. The author provides a unified treatment of the subject, beginning with 16 First Principles on which the theory is based. These are used to establish classical results, such as Rentschler's Theorem for the plane and the Cancellation Theorem for Curves. More recent results, such as Makar-Limanov's theorem for locally nilpotent derivations of polynomial rings, are also discussed. Topics of special interest include progress in classifying additive actions on three-dimensional affine space, finiteness questions (Hilbert's 14th Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem. A lot of new material is included in this expanded second edition, such as canonical factorization of quotient morphisms, and a more extended treatment of linear actions. The reader will also find a wealth of examples and open problems and an updated resource for future investigations.
Author: Teddy Furon
Publisher: Springer
ISBN: 3540773703
Category : Computers
Languages : en
Pages : 402
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Book Description
Researchers and professionals in the field will find the papers in this new volume essential reading. Topically arranged, they cover a multitude of subjects, from new steganographic schemes to computer security and from watermarking to fingerprinting. Complete with online files and updates, this fascinating book constitutes the thoroughly refereed post-proceedings of the 9th International Workshop on Information Hiding, IH 2007, held in Saint Malo, France, in June 2007.
Author: David A. Cox
Publisher: Springer
ISBN: 3319167219
Category : Mathematics
Languages : en
Pages : 664
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Book Description
This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the Preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry—the elimination theorem, the extension theorem, the closure theorem and the Nullstellensatz—this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates a new Chapter (ten), which presents some of the essentials of progress made over the last decades in computing Gröbner bases. The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D). The book may serve as a first or second course in undergraduate abstract algebra and with some supplementation perhaps, for beginning graduate level courses in algebraic geometry or computational algebra. Prerequisites for the reader include linear algebra and a proof-oriented course. It is assumed that the reader has access to a computer algebra system. Appendix C describes features of MapleTM, Mathematica® and Sage, as well as other systems that are most relevant to the text. Pseudocode is used in the text; Appendix B carefully describes the pseudocode used. Readers who are teaching from Ideals, Varieties, and Algorithms, or are studying the book on their own, may obtain a copy of the solutions manual by sending an email to
[email protected]. From the reviews of previous editions: “...The book gives an introduction to Buchberger’s algorithm with applications to syzygies, Hilbert polynomials, primary decompositions. There is an introduction to classical algebraic geometry with applications to the ideal membership problem, solving polynomial equations and elimination theory. ...The book is well-written. ...The reviewer is sure that it will be an excellent guide to introduce further undergraduates in the algorithmic aspect of commutative algebra and algebraic geometry.” —Peter Schenzel, zbMATH, 2007 “I consider the book to be wonderful. ... The exposition is very clear, there are many helpful pictures and there are a great many instructive exercises, some quite challenging ... offers the heart and soul of modern commutative and algebraic geometry.” —The American Mathematical Monthly
Author: Arno van den Essen
Publisher: Springer Science & Business Media
ISBN: 9401585555
Category : Mathematics
Languages : en
Pages : 244
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Book Description
Automorphisms of Affine Spaces describes the latest results concerning several conjectures related to polynomial automorphisms: the Jacobian, real Jacobian, Markus-Yamabe, Linearization and tame generators conjectures. Group actions and dynamical systems play a dominant role. Several contributions are of an expository nature, containing the latest results obtained by the leaders in the field. The book also contains a concise introduction to the subject of invertible polynomial maps which formed the basis of seven lectures given by the editor prior to the main conference. Audience: A good introduction for graduate students and research mathematicians interested in invertible polynomial maps.
