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| Author | : Barbara Fantechi |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 354 |
| Release | : 2005 |
| Genre | : 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. |
| Total Pages | : 498 |
| Release | : 2018-06-01 |
| Genre | : 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 |
| Total Pages | : 292 |
| Release | : 1994 |
| Genre | : 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 | : Bruce E. Meserve |
| Publisher | : Courier Corporation |
| Total Pages | : 340 |
| Release | : 2014-12-08 |
| Genre | : Mathematics |
| ISBN | : 048615226X |
Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.
| Author | : Klaus Hulek |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 225 |
| Release | : 2003 |
| Genre | : 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 | : Solomon Lefschetz |
| Publisher | : Courier Corporation |
| Total Pages | : 250 |
| Release | : 2012-09-05 |
| Genre | : 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 |
| Total Pages | : 324 |
| Release | : 1982-01-01 |
| Genre | : 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.
| Author | : Tamás Szamuely |
| Publisher | : Cambridge University Press |
| Total Pages | : 281 |
| Release | : 2009-07-16 |
| Genre | : Mathematics |
| ISBN | : 0521888506 |
Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.
| Author | : Jakob Stix |
| Publisher | : Springer |
| Total Pages | : 257 |
| Release | : 2012-10-19 |
| Genre | : Mathematics |
| ISBN | : 3642306748 |
The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of its fundamental group. While the conjecture is still open today in 2012, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the Brauer-Manin obstruction is the only one against rational points on curves. This monograph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and the local-to-global approach is studied in detail. The monograph concludes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birational analogue in lieu of the fundamental group extension.
| Author | : Kang Zuo |
| Publisher | : Springer |
| Total Pages | : 142 |
| Release | : 2006-11-14 |
| Genre | : 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.
