Author : Joe Harris
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 39,3 MB
Release : 2013-11-11
Category : 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
Page : 511 pages
File Size : 44,26 MB
Release : 2013-06-29
Category : 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.
Page : 178 pages
File Size : 35,54 MB
Release : 1999
Category : 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
Page : 0 pages
File Size : 26,8 MB
Release : 2023
Category : 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 : G. Kempf
Publisher : Cambridge University Press
Page : 180 pages
File Size : 18,96 MB
Release : 1993-09-09
Category : Mathematics
ISBN : 9780521426138
An introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint.
Author : Shigeru Mukai
Publisher : Cambridge University Press
Page : 528 pages
File Size : 23,15 MB
Release : 2003-09-08
Category : Mathematics
ISBN : 9780521809061
Sample Text
Author : Gerd Fischer
Publisher : Springer Science & Business Media
Page : 153 pages
File Size : 15,50 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3322802175
Ruled varieties are unions of a family of linear spaces. They are objects of algebraic geometry as well as differential geometry, especially if the ruling is developable. This book is an introduction to both aspects, the algebraic and differential one. Starting from very elementary facts, the necessary techniques are developed, especially concerning Grassmannians and fundamental forms in a version suitable for complex projective algebraic geometry. Finally, this leads to recent results on the classification of developable ruled varieties and facts about tangent and secant varieties. Compared to many other topics of algebraic geometry, this is an area easily accessible to a graduate course.
Author : David Mumford
Publisher : Springer
Page : 208 pages
File Size : 11,31 MB
Release : 1976
Category : 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 : Meinolf Geck
Publisher : Oxford University Press
Page : 321 pages
File Size : 50,61 MB
Release : 2013-03-14
Category : 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 Eisenbud
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 27,65 MB
Release : 2006-04-06
Category : 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.
