Affine Algebraic Geometry

Author : Jaime Gutierrez,Vladimir Shpilrain,Jie-Tai Yu
Publisher : American Mathematical Soc.
Page : 288 pages
File Size : 41,8 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821834763

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Affine Algebraic Geometry by Jaime Gutierrez,Vladimir Shpilrain,Jie-Tai Yu Pdf

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.

Author : Kayo Masuda,Hideo Kojima,Takashi Kishimoto
Publisher : World Scientific
Page : 352 pages
File Size : 53,6 Mb
Release : 2013-05-20
Category : Mathematics
ISBN : 9789814436717

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Affine Algebraic Geometry by Kayo Masuda,Hideo Kojima,Takashi Kishimoto Pdf

The present volume grew out of an international conference on affine algebraic geometry held in Osaka, Japan during 3–6 March 2011 and is dedicated to Professor Masayoshi Miyanishi on the occasion of his 70th birthday. It contains 16 refereed articles in the areas of affine algebraic geometry, commutative algebra and related fields, which have been the working fields of Professor Miyanishi for almost 50 years. Readers will be able to find recent trends in these areas too. The topics contain both algebraic and analytic, as well as both affine and projective, problems. All the results treated in this volume are new and original which subsequently will provide fresh research problems to explore. This volume is suitable for graduate students and researchers in these areas. Contents:Acyclic Curves and Group Actions on Affine Toric Surfaces (Ivan Arzhantsev and Mikhail Zaidenberg)Hirzeburch Surfaces and Compactifications of ℂ2 (M Furushima and A Ishida)Cyclic Multiple Planes, Branched Covers of Sn and a Result of D L Goldsmith (R V Gurjar)𝔸1*-Fibrations on Affine Threefolds (R V Gurjar, M Koras, K Masuda, M Miyanishi and P Russell)Miyanishi's Characterization of Singularities Appearing on 𝔸1-Fibrations Does Not Hold in Higher Dimensions (Takashi Kishimoto)A Galois Counterexample to Hilbert's Fourteenth Problem in Dimension Three with Rational Coefficients (Ei Kobayashi and Shigeru Kuroda)Open Algebraic Surfaces of Logarithmic Kodaira Dimension One (Hideo Kojima)Some Properties of ℂ* in ℂ2 (M Koras and P Russell)Abhyankar-Sathaye Embedding Conjecture for a Geometric Case (Tomoaki Ohta)Some Subgroups of the Cremona Groups (Vladimir L Popov)The Gonality of Singular Plane Curves II (Fumio Sakai)Examples of Non-Uniruled Surfaces with Pre-Tango Structures Involving Non-Closed Global Differential 1-Forms (Yoshifumi Takeda)Representations of 𝔾a of Codimension Two (Ryuji Tanimoto)The Projective Characterization of Genus Two Plane Curves Which Have One Place at Infinity (Keita Tono)Sextic Variety as Galois Closure Variety of Smooth Cubic (Hisao Yoshihara)Invariant Hypersurfaces of Endomorphisms of the Projective 3-Space (De-Qi Zhang) Readership: Graduate students and researchers in affine algebraic geometry. Keywords:Affine algebraic geometry;Commutative algebra;Polynomial algebra;Group actions;FibrationsKey Features:Many active researchers such as M Zaidenberg, R V Gurjar, M Koras, P Russell, F Sakai, V Popov, H Yoshihara, and D-Q Zhang contributed articles to this proceedingsMany viewpoints are taken into consideration to study surfaces and threefolds. These will give hints for further research in neighboring fields

Author : Masayoshi Miyanishi
Publisher : World Scientific
Page : 441 pages
File Size : 44,8 Mb
Release : 2023-12-05
Category : Mathematics
ISBN : 9789811280108

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Affine Algebraic Geometry: Geometry Of Polynomial Rings by Masayoshi Miyanishi Pdf

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 : Rajendra V. Gurjar,Kayo Masuda,Masayoshi Miyanishi
Publisher : Walter de Gruyter GmbH & Co KG
Page : 360 pages
File Size : 43,8 Mb
Release : 2021-07-05
Category : Mathematics
ISBN : 9783110577563

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Affine Space Fibrations by Rajendra V. Gurjar,Kayo Masuda,Masayoshi Miyanishi Pdf

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.

Author : 健爾·上野,上野健爾
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 44,6 Mb
Release : 1999
Category : Geometry, Algebraic
ISBN : 9780821808627

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Algebraic Geometry 1 by 健爾·上野,上野健爾 Pdf

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.

Author : Daniel Daigle,Richard Ganong,Mariusz Koras
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 54,8 Mb
Release : 2011-01-01
Category : Mathematics
ISBN : 9780821883839

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Affine Algebraic Geometry by Daniel Daigle,Richard Ganong,Mariusz Koras Pdf

Author : Kenji Ueno
Publisher : American Mathematical Soc.
Page : 180 pages
File Size : 52,8 Mb
Release : 1999
Category : Mathematics
ISBN : 0821808621

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Algebraic Geometry 1 by Kenji Ueno Pdf

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.

Author : Peter Falb
Publisher : Springer
Page : 202 pages
File Size : 55,5 Mb
Release : 2018-08-25
Category : Mathematics
ISBN : 9783319980263

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Methods of Algebraic Geometry in Control Theory: Part I by Peter Falb Pdf

"An introduction to the ideas of algebraic geometry in the motivated context of system theory." Thus the author describes his textbook that has been specifically written to serve the needs of students of systems and control. Without sacrificing mathematical care, the author makes the basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis is on constructive methods and clarity rather than abstraction. The student will find here a clear presentation with an applied flavor, of the core ideas in the algebra-geometric treatment of scalar linear system theory. The author introduces the four representations of a scalar linear system and establishes the major results of a similar theory for multivariable systems appearing in a succeeding volume (Part II: Multivariable Linear Systems and Projective Algebraic Geometry). Prerequisites are the basics of linear algebra, some simple notions from topology and the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises are an integral part of the treatment and are used where relevant in the main body of the text. The present, softcover reprint is designed to make this classic textbook available to a wider audience. "This book is a concise development of affine algebraic geometry together with very explicit links to the applications...[and] should address a wide community of readers, among pure and applied mathematicians." —Monatshefte für Mathematik

Author : Meinolf Geck
Publisher : Oxford University Press
Page : 321 pages
File Size : 42,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9780199676163

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An Introduction to Algebraic Geometry and Algebraic Groups by Meinolf Geck Pdf

An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields.

Author : J. S. Milne
Publisher : Allied Publishers
Page : 232 pages
File Size : 55,9 Mb
Release : 2012
Category : Geometry, Algebraic
ISBN : 8177644548

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Algebraic Geometry by J. S. Milne Pdf

Author : Shigeru Kuroda,Nobuharu Onoda,Gene Freudenburg
Publisher : Springer Nature
Page : 317 pages
File Size : 54,8 Mb
Release : 2020-03-27
Category : Mathematics
ISBN : 9783030421366

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Polynomial Rings and Affine Algebraic Geometry by Shigeru Kuroda,Nobuharu Onoda,Gene Freudenburg Pdf

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 : D. G. Northcott
Publisher : Cambridge University Press
Page : 297 pages
File Size : 53,6 Mb
Release : 1980-05-08
Category : Mathematics
ISBN : 9780521229098

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Affine Sets and Affine Groups by D. G. Northcott Pdf

In these notes, first published in 1980, Professor Northcott provides a self-contained introduction to the theory of affine algebraic groups for mathematicians with a basic knowledge of communicative algebra and field theory. The book divides into two parts. The first four chapters contain all the geometry needed for the second half of the book which deals with affine groups. Alternatively the first part provides a sure introduction to the foundations of algebraic geometry. Any affine group has an associated Lie algebra. In the last two chapters, the author studies these algebras and shows how, in certain important cases, their properties can be transferred back to the groups from which they arose. These notes provide a clear and carefully written introduction to algebraic geometry and algebraic groups.

Author : Daniel Bump
Publisher : World Scientific
Page : 232 pages
File Size : 50,5 Mb
Release : 1998
Category : Mathematics
ISBN : 9810235615

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Algebraic Geometry by Daniel Bump Pdf

This is a graduate-level text on algebraic geometry that provides a quick and fully self-contained development of the fundamentals, including all commutative algebra which is used. A taste of the deeper theory is given: some topics, such as local algebra and ramification theory, are treated in depth. The book culminates with a selection of topics from the theory of algebraic curves, including the Riemann-Roch theorem, elliptic curves, the zeta function of a curve over a finite field, and the Riemann hypothesis for elliptic curves.

Author : Peter Russell,Daniel Daigle,Richard Ganong,Mariusz Koras
Publisher : American Mathematical Soc.
Page : 334 pages
File Size : 49,8 Mb
Release : 2011
Category : Mathematics
ISBN : 0821872834

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Affine Algebraic Geometry by Peter Russell,Daniel Daigle,Richard Ganong,Mariusz Koras Pdf

This volume grew out of an international conference which was held in June 2009 at McGill University, in honour of Professor Peter Russell, on the occasion of his 70th birthday and his retirement from McGill. It contains 19 refereed articles, essentially all in the area of affine algebraic geometry and, more specifically, in the following subjects: automorphisms and group actions, surfaces, embeddings of certain rational curves in the affine plane, and problems in positive characteristic geometry. These are also some of the themes running through the very substantial body of work done by Professor Russell in this relatively young branch of algebraic geometry. The volume also includes a foreword, in which Professor Russell shares some personal reminiscences on the development of affine algebraic geometry, a field he describes as ``loosely speaking, the study of affine spaces and algebraic varieties closely resembling them.''

Author : Robin Hartshorne
Publisher : Springer Science & Business Media
Page : 511 pages
File Size : 46,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475738490

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Algebraic Geometry by Robin Hartshorne Pdf

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.