Algebraic Geometry Iv
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Author |
: A.N. Parshin |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 291 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783662030738 |
ISBN-13 |
: 366203073X |
Rating |
: 4/5 (38 Downloads) |
Synopsis Algebraic Geometry IV by : A.N. Parshin
Two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory, by well-known experts in the fields. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics.
Author |
: Yurĭi Grigorevǐc Reshetnyak |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 274 |
Release |
: 1993-10-14 |
ISBN-10 |
: 3540547010 |
ISBN-13 |
: 9783540547013 |
Rating |
: 4/5 (10 Downloads) |
Synopsis Geometry IV by : Yurĭi Grigorevǐc Reshetnyak
This book contains two surveys on modern research into non-regular Riemannian geometry, carried out mostly by Russian mathematicians. Coverage examines two-dimensional Riemannian manifolds of bounded curvature and metric spaces whose curvature lies between two given constants. This book will be immensely useful to graduate students and researchers in geometry, in particular Riemannian geometry.
Author |
: Igor V. Dolgachev |
Publisher |
: Cambridge University Press |
Total Pages |
: 653 |
Release |
: 2012-08-16 |
ISBN-10 |
: 9781139560788 |
ISBN-13 |
: 1139560786 |
Rating |
: 4/5 (88 Downloads) |
Synopsis Classical Algebraic Geometry by : Igor V. Dolgachev
Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.
Author |
: John Stillwell |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 240 |
Release |
: 2005-08-09 |
ISBN-10 |
: 9780387255309 |
ISBN-13 |
: 0387255303 |
Rating |
: 4/5 (09 Downloads) |
Synopsis The Four Pillars of Geometry by : John Stillwell
This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic Abundantly supplemented with figures and exercises
Author |
: Robin Hartshorne |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 511 |
Release |
: 2013-06-29 |
ISBN-10 |
: 9781475738490 |
ISBN-13 |
: 1475738498 |
Rating |
: 4/5 (90 Downloads) |
Synopsis Algebraic Geometry by : Robin Hartshorne
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.
Author |
: S. K. Donaldson |
Publisher |
: Oxford University Press |
Total Pages |
: 464 |
Release |
: 1997 |
ISBN-10 |
: 0198502699 |
ISBN-13 |
: 9780198502692 |
Rating |
: 4/5 (99 Downloads) |
Synopsis The Geometry of Four-manifolds by : S. K. Donaldson
This text provides an accessible account to the modern study of the geometry of four-manifolds. Prerequisites are a firm grounding in differential topology and geometry, as may be gained from the first year of a graduate course.
Author |
: Serge Lang |
Publisher |
: Courier Dover Publications |
Total Pages |
: 273 |
Release |
: 2019-03-20 |
ISBN-10 |
: 9780486839806 |
ISBN-13 |
: 048683980X |
Rating |
: 4/5 (06 Downloads) |
Synopsis Introduction to Algebraic Geometry by : Serge Lang
Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.
Author |
: Qing Liu |
Publisher |
: Oxford University Press |
Total Pages |
: 593 |
Release |
: 2006-06-29 |
ISBN-10 |
: 9780191547805 |
ISBN-13 |
: 0191547808 |
Rating |
: 4/5 (05 Downloads) |
Synopsis Algebraic Geometry and Arithmetic Curves by : Qing Liu
This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the funadmental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.
Author |
: David Mumford |
Publisher |
: Springer |
Total Pages |
: 316 |
Release |
: 2004-02-21 |
ISBN-10 |
: 9783540460213 |
ISBN-13 |
: 3540460217 |
Rating |
: 4/5 (13 Downloads) |
Synopsis The Red Book of Varieties and Schemes by : David Mumford
Mumford's famous "Red Book" gives a simple, readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduates or mathematicians in other fields wishing to quickly learn aboutalgebraic geometry. This new edition includes an appendix that gives an overview of the theory of curves, their moduli spaces and their Jacobians -- one of the most exciting fields within algebraic geometry.
Author |
: Wolfram Decker |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 331 |
Release |
: 2006-03-02 |
ISBN-10 |
: 9783540289920 |
ISBN-13 |
: 3540289925 |
Rating |
: 4/5 (20 Downloads) |
Synopsis Computing in Algebraic Geometry by : Wolfram Decker
This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations. Originating from a number of intense one week schools taught by the authors, the text is designed so as to provide a step by step introduction which enables the reader to get started with his own computational experiments right away. The authors present the basic concepts and ideas in a compact way.