Author : Barbara Fantechi
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 44,39 MB
Release : 2005
Category : Mathematics
ISBN : 0821842455
Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.
Author : Steven Dale Cutkosky
Publisher : American Mathematical Soc.
Page : 498 pages
File Size : 17,46 MB
Release : 2018-06-01
Category : Mathematics
ISBN : 1470435187
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.
Author : Igor Rostislavovich Shafarevich
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 20,77 MB
Release : 1994
Category : Mathematics
ISBN : 9783540575542
The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds. As with Volume 1 the author has revised the text and added new material, e.g. a section on real algebraic curves. Although the material is more advanced than in Volume 1 the algebraic apparatus is kept to a minimum making the book accessible to non-specialists. It can be read independently of Volume 1 and is suitable for beginning graduate students in mathematics as well as in theoretical physics.
Author : Klaus Hulek
Publisher : American Mathematical Soc.
Page : 225 pages
File Size : 31,18 MB
Release : 2003
Category : Mathematics
ISBN : 0821829521
This book is a true introduction to the basic concepts and techniques of algebraic geometry. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory. The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary.
Author : Robin Hartshorne
Publisher : Springer Science & Business Media
Page : 511 pages
File Size : 48,30 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 : Kang Zuo
Publisher : Springer
Page : 142 pages
File Size : 50,6 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540484248
Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry and non-linear analysis. This book can form the basis for graduate level seminars in the area of topology of algebraic varieties. It also contains present new techniques for researchers working in this area.
Author : Miles Reid
Publisher : Cambridge University Press
Page : 144 pages
File Size : 47,43 MB
Release : 1988-12-15
Category : 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.
Author : Tamás Szamuely
Publisher : Cambridge University Press
Page : 281 pages
File Size : 39,6 MB
Release : 2009-07-16
Category : Mathematics
ISBN : 0521888506
Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.
Author : Solomon Lefschetz
Publisher : Courier Corporation
Page : 250 pages
File Size : 21,82 MB
Release : 2012-09-05
Category : Mathematics
ISBN : 0486154726
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Author : Bruce Elwyn Meserve
Publisher : Courier Corporation
Page : 324 pages
File Size : 39,55 MB
Release : 1982-01-01
Category : Mathematics
ISBN : 9780486614700
Uncommonly interesting introduction illuminates complexities of higher mathematics while offering a thorough understanding of elementary mathematics. Covers development of complex number system and elementary theories of numbers, polynomials and operations, determinants, matrices, constructions and graphical representations. Several exercises — without solutions.
