introduction to algebraic geometry

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Introduction To Algebraic Geometry

Author : Brendan Hassett
ISBN : 9781139464598
Genre : Mathematics
File Size : 35. 73 MB
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Algebraic geometry, central to pure mathematics, has important applications in such fields as engineering, computer science, statistics and computational biology, which exploit the computational algorithms that the theory provides. Users get the full benefit, however, when they know something of the underlying theory, as well as basic procedures and facts. This book is a systematic introduction to the central concepts of algebraic geometry most useful for computation. Written for advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and restricts development of formalism to what is needed to address these examples. In particular, it introduces the notion of Gröbner bases early on and develops algorithms for almost everything covered. It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer science, biomathematics and bioinformatics.

Introduction To Algebraic Geometry

Author : Justin R. Smith
ISBN : 9781503381537
Genre : Geometry, Algebraic
File Size : 86. 43 MB
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This book is intended for self-study or as a textbook for graduate students or advanced undergraduates. It presupposes some basic knowledge of point-set topology and a solid foundation in linear algebra. Otherwise, it develops all of the commutative algebra, sheaf-theory and cohomology needed to understand the material. It also presents applications to robotics and other fields.

An Introduction To Algebraic Geometry

Author : Kenji Ueno
ISBN : 9780821811443
Genre : Mathematics
File Size : 27. 61 MB
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This introduction to algebraic geometry allows readers to grasp the fundamentals of the subject with only linear algebra and calculus as prerequisites. After a brief history of the subject, the book introduces projective spaces and projective varieties, and explains plane curves and resolution of their singularities. The volume further develops the geometry of algebraic curves and treats congruence zeta functions of algebraic curves over a finite field. It concludes with a complex analytical discussion of algebraic curves. The author emphasizes computation of concrete examples rather than proofs, and these examples are discussed from various viewpoints. This approach allows readers to develop a deeper understanding of the theorems.

Algebraic Geometry

Author : Robin Hartshorne
ISBN : 9781475738490
Genre : Mathematics
File Size : 32. 97 MB
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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.

Introduction To Algebraic Geometry And Algebraic Groups

Author :
ISBN : 008087150X
Genre : Mathematics
File Size : 41. 56 MB
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Introduction to Algebraic Geometry and Algebraic Groups

Algebraic Curves

Author : William Fulton
ISBN : UOM:39015050421349
Genre : Mathematics
File Size : 36. 60 MB
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An Introduction To Algebraic Geometry And Algebraic Groups

Author : Meinolf Geck
ISBN : 9780191663727
Genre : Mathematics
File Size : 49. 61 MB
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An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles. Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type. The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, a thorough treatment of Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields. Experts in the field will enjoy some of the new approaches to classical results. The text uses algebraic groups as the main examples, including worked out examples, instructive exercises, as well as bibliographical and historical remarks.

Introduction To Algebraic Geometry

Author : Serge Lang
ISBN : 1614276277
Genre : Literary Collections
File Size : 50. 13 MB
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2014 Reprint of 1958 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This book, an introduction to the Weil-Zariski algebraic geometry, is an amplification of lectures for one of a series of courses, given by various people, going back to Zariski. Restricted to qualitative algebraic geometry, it is an admirable introduction to Weil's "Foundations" and, more generally, the whole of the modern literature as it existed before the advent of sheaves.

Introduction To Algebraic Geometry And Commutative Algebra

Author : Dilip P. Patil
ISBN : 9789814304573
Genre : Mathematics
File Size : 38. 1 MB
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Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. With concise yet clear definitions and synopses a selection is made from the wealth of meterial in the disciplines including the Riemann-Roch theorem for arbitrary projective curves."--pub. desc.

Introduction To Algebraic Geometry

Author : Steven Dale Cutkosky
ISBN : 1470435187
Genre : Geometry, Algebraic
File Size : 24. 93 MB
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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 $0$ 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.

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