A First Course In Algebraic Geometry And Algebraic Varieties
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| Author | : Joe Harris |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 344 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 1475721897 |
"This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship." --MATHEMATICAL REVIEWS
| Author | : Robin Hartshorne |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 511 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475738498 |
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 | : Kenji Ueno |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 178 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 0821808621 |
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 | : Flaminio Flamini |
| Publisher | : World Scientific Publishing Europe Limited |
| Total Pages | : 0 |
| Release | : 2023 |
| Genre | : Geometry, Algebraic |
| ISBN | : 9781800612747 |
"This book provides a gentle introduction to the foundations of Algebraic Geometry, starting from computational topics (ideals and homogeneous ideals, zero loci of ideals) up to increasingly intrinsic and abstract arguments, like "Algebraic Varieties", whose natural continuation is a more advanced course on the theory of schemes, vector bundles and sheaf-cohomology. Valuable to students studying Algebraic Geometry and Geometry, A First Course in Algebraic Geometry and Algebraic Varieties contains around 60 solved exercises to help students thoroughly understand the theories introduced in the book. Proofs of the results are carried out in full details. Many examples are discussed which reinforces the understanding of both the theoretical elements and their consequences as well as the possible applications of the material"--
| Author | : Shigeru Mukai |
| Publisher | : Cambridge University Press |
| Total Pages | : 528 |
| Release | : 2003-09-08 |
| Genre | : Mathematics |
| ISBN | : 9780521809061 |
| Author | : Meinolf Geck |
| Publisher | : Oxford University Press |
| Total Pages | : 321 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 019967616X |
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 | : David Mumford |
| Publisher | : Springer |
| Total Pages | : 208 |
| Release | : 1976 |
| Genre | : Mathematics |
| ISBN | : |
From the reviews: "Although several textbooks on modern algebraic geometry have been published in the meantime, Mumford's "Volume I" is, together with its predecessor the red book of varieties and schemes, now as before one of the most excellent and profound primers of modern algebraic geometry. Both books are just true classics!" Zentralblatt
| Author | : David Eisenbud |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 265 |
| Release | : 2006-04-06 |
| Genre | : Mathematics |
| ISBN | : 0387226397 |
Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
| Author | : Ernst Kunz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 253 |
| Release | : 2012-11-06 |
| Genre | : Mathematics |
| ISBN | : 1461459877 |
Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.
| Author | : Miles Reid |
| Publisher | : Cambridge University Press |
| Total Pages | : 144 |
| Release | : 1988-12-15 |
| Genre | : Mathematics |
| ISBN | : 9780521356626 |
Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time. With the minimum of prerequisites, Dr Reid introduces the reader to the basic concepts of algebraic geometry including: plane conics, cubics and the group law, affine and projective varieties, and non-singularity and dimension. He is at pains to stress the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book arises from an undergraduate course given at the University of Warwick and contains numerous examples and exercises illustrating the theory.
