Algebraic Geometry for Scientists and Engineers


Author: Shreeram Shankar Abhyankar

Publisher: American Mathematical Soc.

ISBN: 0821815350

Category: Mathematics

Page: 295

View: 4430

This book, based on lectures presented in courses on algebraic geometry taught by the author at Purdue University, is intended for engineers and scientists (especially computer scientists), as well as graduate students and advanced undergraduates in mathematics. In addition to providing a concrete or algorithmic approach to algebraic geometry, the author also attempts to motivate and explain its link to more modern algebraic geometry based on abstract algebra.The book covers various topics in the theory of algebraic curves and surfaces, such as rational and polynomial parametrization, functions and differentials on a curve, branches and valuations, and resolution of singularities. The emphasis is on presenting heuristic ideas and suggestive arguments rather than formal proofs. Readers will gain new insight into the subject of algebraic geometry in a way that should increase appreciation of modern treatments of the subject, as well as enhance its utility in applications in science and industry.

Introduction to Algebraic Geometry


Author: Steven Dale Cutkosky

Publisher: American Mathematical Soc.

ISBN: 1470435187

Category: Geometry, Algebraic

Page: 484

View: 3482

This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters. With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.

Computational Methods in Commutative Algebra and Algebraic Geometry


Author: Wolmer Vasconcelos

Publisher: Springer Science & Business Media

ISBN: 9783540213116

Category: Mathematics

Page: 408

View: 3909

This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.

Computational Approach to Riemann Surfaces


Author: Alexander I. Bobenko,Christian Klein

Publisher: Springer Science & Business Media

ISBN: 3642174124

Category: Mathematics

Page: 257

View: 1588

This volume is a well structured overview of existing computational approaches to Riemann surfaces as well as those under development. It covers the software tools currently available and provides solutions to partial differential equations and surface theory.

Commutative Algebra - Proceedings Of The Workshop


Author: Valla Giuseppe,Trung Ngo Viet,Simis Aron

Publisher: World Scientific

ISBN: 9814551791


Page: 328

View: 2485

In a relatively short time, commutative algebra has grown in many directions. Over a period of nearly fifty years starting from the so-called homological period till today, the area has developed into a rich laboratory of methods, structures and problem-solving tools.One could say a distinct modern trend of commutative algebra is a strong interaction with various aspects of Combinatorics and Computer Algebra. This has resulted in a new sense of measuring for old assumptions, and a better understanding of old results.At the same time, Invariant Theory and Algebraic Geometry remain constituents of an everlasting classical source, responsible for important themes that have been developed in Commutative Algebra — such as deformation, linkage, algebraic tori and determinantal rings, etc.This volume of proceedings is well-entrenched on the lines of development outlined above. As such, it aims to keep researchers and mathematicians well-informed of the developments in the field.

Algebraic Curves over a Finite Field


Author: J. W.P. Hirschfeld,G. Korchmáros,F. Torres

Publisher: Princeton University Press

ISBN: 1400847419

Category: Mathematics

Page: 744

View: 7567

This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.

Algebraic geometry and its applications

collections of papers from Shreeram S. Abhyankar's 60th birthday conference


Author: Shreeram Shankar Abhyankar,Chanderjit Bajaj

Publisher: Springer

ISBN: 9783540941767

Category: Mathematics

Page: 536

View: 796

Geometry and analysis

papers presented at the Bombay Colloquium 1992


Author: Shreeram Shankar Abhyankar,Tata Institute of Fundamental Research

Publisher: Oxford University Press, USA


Category: Mathematics

Page: 312

View: 6311

This volume consists of articles based on lectures delivered at an International Colloquium held at the Tata Institute of Fundamental Research, Bombay. Experts from all over the world spoke at the Conference on different aspects of geometry and analysis. Topics include: impact of geometry on the boundary solutions of a semilinear Neumann problem with critical nonlinearity; algebraic representations of reductive groups over local fields; scalar conservation laws with boundary condition; and the Borel-Weil theorem and the Feynman path integral. 1. Fundamental group of the Affine Line in Positive Characteristic, S.S. Abhyankar 2. Impact of geometry on the boundary on the positive solutions of a semilinear Neumann problem with Critical nonlinearity, Adimurthi 3. Sur a cohomologie de certains espaces de modules de fibres fectoriels, A. Beauville 4. Some quantum analogues of solvable Lie groups, C. De Concini et al 5. Compact complex manifolds whose tangent bundles satisfy numerical effectivity properties, J.-P. Demailly 6. Algebraic Representations of Reductive Groups over Local Fields, W.J. Haboush 7. Poncelet Polygons and the Painleve Equations, N.J. Hitchin 8. Scalar conservation laws with boundary condition, K.T. Joseph 9. Bases for Quantum Demazure modules-I, V. Lakshmibai 10. An Appendix to Basesfor Quantum Demazurew modules-I 11. Moduli Spaces of Abelian Surfaces with Isogeny, Ch. Birkenhake and H. Lange 12. Instantons and Parabolic Sheaves, M. Maruyama 13. Numerically effective line bundles which are not ample, V.B. Mehta and S. Subramanian 14. Moduli of logarithmic connections, N. Nitsure 15. The Borel-Weil theorem and the Feyman path integral, K. Okamoto 16. Geometric super-rigidity, Y.-T. Siu

Vorlesungen über Algebraische Geometrie

Geometrie auf einer Kurve Riemannsche Flächen Abelsche Integrale


Author: Dr. Francesco Severi

Publisher: Springer-Verlag

ISBN: 3663157733

Category: Mathematics

Page: 408

View: 6161

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Kähler Differentials


Author: Ernst Kunz

Publisher: Vieweg+Teubner Verlag

ISBN: 9783528089733

Category: Mathematics

Page: 402

View: 3103

This book is based on a lecture course that I gave at the University of Regensburg. The purpose of these lectures was to explain the role of Kähler differential forms in ring theory, to prepare the road for their application in algebraic geometry, and to lead up to some research problems. The text discusses almost exclusively local questions and is therefore written in the language of commutative alge bra. The translation into the language of algebraic geometry is easy for the reader who is familiar with sheaf theory and the theory of schemes. The principal goals of the monograph are: To display the information contained in the algebra of Kähler differential forms (de Rham algebra) of a commutative algebra, to int- duce and discuss "differential invariants" of algebras, and to prove theorems about algebras with "differential methods". The most important object we study is the module of Kähler differentials n~/R of an algebra SIR. Like the differentials of analysis, differential modules "linearize" problems, i.e. reduce questions about algebras (non-linear problems) to questions of linear algebra. We are mainly interested in algebras of finite type.

Lehr- und Wanderjahre eines Mathematikers

Aus dem Französischen von Theresia Übelhör


Author: André Weil

Publisher: Springer-Verlag

ISBN: 3034850476

Category: Science

Page: 212

View: 4610

Mein Leben, oder zumindest das, was diesen Namen verdient -ein außer gewöhnlich glückliches Leben mit einigen Schicksalsschlägen -erstreckte sich auf die Zeit zwischen dem 6. Mai 1906, dem Tag meiner Geburt, und dem 24. Mai 1986, dem Todestag meiner Frau und Gefährtin Eveline. Wenn auf diesen Seiten, die ihr gewidmet sind, von meiner Frau recht wenig die Rede sein wird, heißt das nicht, daß sie in meinem Leben und in meinen Gedanken einen geringen Platz eingenommen hätte. Sie war im Gegenteil, beinahe vom Tag unserer ersten Begegnung an, so eng damit verwoben, daß von mir oder von ihr zu sprechen ein und dasselbe ist. Ihre Anwesenheit beziehungsweise ihre Abwesenheit bestimmte die Textur meines ganzen Lebens. Was könnte ich anderes dazu sagen, als daß unsere Ehe eine von jenen war, die La Rochefoucauld Lügen strafen? »Fulsere vere candidi mihi soles . . . . « Ebenso wird meine Schwester kaum erwähnt werden. Es ist schon lange her, daß ich meine Erinnerungen an sie Simone Petrement mitgeteilt habe, die sie in ihre gute Biographie La vie de Simone Weil einfließen ließ, wo man viele Einzelheiten über unsere gemeinsame Kindheit erfahren kann, und es wäre unnötig, dies hier zu wiederholen. Als Kinder waren wir unzertrennlich, aber ich war der große Bruder und sie die kleine Schwester. Später waren wir selten zusammen, und meist sprachen wir in scherzhaftem Ton miteinander, denn sie hatte ein fröhliches und humorvolles Naturell, wie alle, die sie kannten, bestätigt haben.

Das BUCH der Beweise


Author: Martin Aigner,Günter M. Ziegler

Publisher: Springer-Verlag

ISBN: 3662064545

Category: Mathematics

Page: 247

View: 2120

Die elegantesten mathematischen Beweise, spannend und für jeden Interessierten verständlich. "Der Beweis selbst, seine Ästhetik, seine Pointe geht ins Geschichtsbuch der Königin der Wissenschaften ein. Ihre Anmut offenbart sich in dem gelungenen und geschickt illustrierten Buch." Die Zeit