Download or read book Polynomial Rings and Affine Spaces written by Masayoshi Nagata and published by American Mathematical Soc.. This book was released on 1978 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Affine Algebraic Geometry Geometry Of Polynomial Rings written by Masayoshi Miyanishi and published by World Scientific. This book was released on 2023-12-05 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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:
Download or read book Polynomial Rings and Affine Algebraic Geometry written by Shigeru Kuroda and published by Springer Nature. This book was released on 2020-03-27 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Automorphisms of Affine Spaces written by Arno van den Essen and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Polynomial Rings and Affine Algebraic Geometry written by Shigeru Kuroda and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume gathers together selected, peer-reviewed works presented at the Polynomial Rings and Affine Algebraic Geometry conference which was held at the Tokyo Metropolitan University on February 12-26, 2018, in Tokyo, Japan. In this book, the reader will find some of the latest research conducted by an international group of experts in affine and projective algebraic geometry. 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. The articles contained in this volume will be of interest to all researchers and graduate students working in the fields of affine and projective algebraic geometry, as well as in certain aspects of commutative algebra, Lie theory, symplectic geometry and Stein manifolds.
Download or read book Tackling Problems on Affine Space with Locally Nilpotent Derivations on Polynomial Rings written by Petrus Johannes Bernardus van Rossum and published by . This book was released on 2001 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Affine Space Fibrations written by Rajendra V. Gurjar and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-07-05 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Affine algebraic geometry has progressed remarkably in the last half a century, and its central topics are affine spaces and affine space fibrations. This authoritative book is aimed at graduate students and researchers alike, and studies the geometry and topology of morphisms of algebraic varieties whose general fibers are isomorphic to the affine space while describing structures of algebraic varieties with such affine space fibrations.
Download or read book Affine Algebraic Geometry written by Jaime Gutierrez and published by American Mathematical Soc.. This book was released on 2005 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Special Session on affine and algebraic geometry took place at the first joint meeting between the American Mathematical Society (AMS) and the Real Sociedad Matematica Espanola (RSME) held in Seville (Spain). This volume contains articles by participating speakers at the Session. The book contains research and survey papers discussing recent progress on the Jacobian Conjecture and affine algebraic geometry and includes a large collection of open problems. It is suitable for graduate students and research mathematicians interested in algebraic geometry.
Download or read book Rings Polynomials and Modules written by Marco Fontana and published by Springer. This book was released on 2017-11-11 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of articles highlighting recent developments in commutative algebra and related non-commutative generalizations. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non-Noetherian ring theory, module theory and integer-valued polynomials along with connections to algebraic number theory, algebraic geometry, topology and homological algebra. Most of the eighteen contributions are authored by attendees of the two conferences in commutative algebra that were held in the summer of 2016: “Recent Advances in Commutative Ring and Module Theory,” Bressanone, Italy; “Conference on Rings and Polynomials” Graz, Austria. There is also a small collection of invited articles authored by experts in the area who could not attend either of the conferences. Following the model of the talks given at these conferences, the volume contains a number of comprehensive survey papers along with related research articles featuring recent results that have not yet been published elsewhere.
Download or read book Rings with Polynomial Identities and Finite Dimensional Representations of Algebras written by Eli Aljadeff and published by American Mathematical Soc.. This book was released on 2020-12-14 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: A polynomial identity for an algebra (or a ring) A A is a polynomial in noncommutative variables that vanishes under any evaluation in A A. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike. The book is divided into four parts. Part 1 contains foundational material on representation theory and noncommutative algebra. In addition to setting the stage for the rest of the book, this part can be used for an introductory course in noncommutative algebra. An expert reader may use Part 1 as reference and start with the main topics in the remaining parts. Part 2 discusses the combinatorial aspects of the theory, the growth theorem, and Shirshov's bases. Here methods of representation theory of the symmetric group play a major role. Part 3 contains the main body of structure theorems for PI algebras, theorems of Kaplansky and Posner, the theory of central polynomials, M. Artin's theorem on Azumaya algebras, and the geometric part on the variety of semisimple representations, including the foundations of the theory of Cayley–Hamilton algebras. Part 4 is devoted first to the proof of the theorem of Razmyslov, Kemer, and Braun on the nilpotency of the nil radical for finitely generated PI algebras over Noetherian rings, then to the theory of Kemer and the Specht problem. Finally, the authors discuss PI exponent and codimension growth. This part uses some nontrivial analytic tools coming from probability theory. The appendix presents the counterexamples of Golod and Shafarevich to the Burnside problem.
Download or read book Polynomial and Affine Spaces written by Masayoshi Nagata and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Geometry 1 written by Kenji Ueno and published by American Mathematical Soc.. This book was released on 1999 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: By studying algebraic varieties over a field, this book demonstrates how the notion of schemes is necessary in algebraic geometry. It gives a definition of schemes and describes some of their elementary properties.
Download or read book Algebraic Theory of Locally Nilpotent Derivations written by Gene Freudenburg and published by Springer. This book was released on 2017-09-08 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebraic Spaces written by Michael Artin and published by . This book was released on 1969 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Information Hiding written by Teddy Furon and published by Springer. This book was released on 2008-01-04 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Ideals Varieties and Algorithms written by David A. Cox and published by Springer. This book was released on 2015-04-30 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Algebraic Geometry 1 written by Kenji Ueno and published by American Mathematical Soc.. This book was released on 1999 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: By studying algebraic varieties over a field, this book demonstrates how the notion of schemes is necessary in algebraic geometry. It gives a definition of schemes and describes some of their elementary properties.
