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61. Global Geometry and Mathematical Physics: Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held at Montecatini ... Mathematics / Fondazione C.I.M.E., Firenze) by L. Alvarez-Gaume, E. Arbarello, C. De Concini, N.J. Hitchin | |
Paperback: 197
Pages
(1990-12-03)
list price: US$26.00 -- used & new: US$22.44 (price subject to change: see help) Asin: 3540532862 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
62. The Geometry of Schemes (Graduate Texts in Mathematics) (Volume 0) by David Eisenbud, Joe Harris | |
Paperback: 312
Pages
(2000-01-25)
list price: US$49.95 -- used & new: US$40.39 (price subject to change: see help) Asin: 0387986375 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description This book is intended to bridge the chasm between a first course in classical algebraic geometry and a technical treatise on schemes. It focuses on examples, and strives to show "what is going on" behind the definitions. There are many exercises to test and extend the reader's understanding. The prerequisites are modest: a little commutative algebra and an acquaintance with algebraic varieties, roughly at the level of a one-semester course. The book aims to show schemes in relation to other geometric ideas, such as the theory of manifolds. Some familiarity with these ideas is helpful, though not required. Customer Reviews (6)
Good book!
Supplement
good for a diffrent point of few.
Crystal clear overview of a traditionally abstract subject In chapter 1, the main definitions are given and the basic concepts behind schemes outlined. That schemes are more complicated than varieties is readily apparent even in this beginning chapter, where they are thought of as corresponding to the spectrum of a commutative ring with identity. Very elementary exercises are given to help the reader gain confidence in the constructions involved. They authors do have to discuss some sheaf theory, but they show its relevance nicely in this chapter. They also discuss the notion of a fibered product as a generalization of the idea of a preimage of a set under the application of a function and relate it to the construction of the functor of points. The role of the functor of points as reducing schemes to a kind of set theory is brought out beautifully here. The next chapter gives many examples of schemes, with the first examples being reduced schemes over algebraically closed fields, these being essentially the ordinary varieties of classical algebraic geometry. The authors then give examples of schemes, the local schemes, which are more general than varieties. When departing from the assumption of a field that is not finitely generated, extra points will have to be added to classical varieties. The fact that only one closed point appears is compared to the case of complex manifolds, via the concept of a germ. This is a very helpful comparison, and one that further solidifies the understanding of a scheme in the mind of the reader. The authors give the reader a short peek at the etale topology in one of the examples. Examples are then given where the field is not algebraically closed, generalizing classical number theory, and non-reduced schemes, where nilpotents are present. The chapter ends with examples of arithmetic schemes where the spectra of rings are finitely generated over the integers. Projective schemes are the subject of Chapter 3, and are defined in terms of graded algebras and invariants of projective schemes embedded in projective space are discussed. The Grasmannian scheme is discussed in detail as an example of a projective scheme. Interestingly, Bezout's theorem, very familiar from elementary algebraic geometry, is generalized here to projective schemes. Constructions from classical algebraic geometry are generalized to schemes in Chapter 4. The first one discussed is the notion of a flex, which deals (classically) with the locus of tangent lines to a variety. The flexes are defined in terms of the Hessian of the variety, the latter being generalized by the authors to define a scheme of flexes. The notion of blowing up is also generalized to the scheme setting, with the authors motivating the discussion by blowing up the plane. The discussion of blow-ups along non-reduced subschemes of a scheme and blow-ups of arithmetic schemes is fascinating and the presentation is crystal clear. Fano varieties are also generalized to Fano schemes in the chapter. Most of the information about these schemes are contained in the exercises, and some of these need to be worked out for a thorough understanding. The next chapter is more categorical in nature, and deals with generalizations of the classical Sylvester construction of resultants and discriminants to the scheme setting. In the last chapter the authors return to the functor of points, and motivate the discussion by asking for a parametrization of families of schemes. The authors show, interestingly, that using the functor of points one can more easily compute geometric information about a scheme than using its equations. They illustrate this for the Zariski tangent space. Then after an overview of Hilbert schemes they close the book by introducing the reader to moduli spaces and a hint of algebraic stacks. No end in sight for this beautiful subject..........
A very good start |
63. Topological Methods in Algebraic Geometry (Classics in Mathematics) by Friedrich Hirzebruch | |
Paperback: 234
Pages
(1995-02-24)
list price: US$59.95 -- used & new: US$48.31 (price subject to change: see help) Asin: 3540586636 Canada | United Kingdom | Germany | France | Japan | |
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64. Quadratic Forms with Applications to Algebraic Geometry and Topology (London Mathematical Society Lecture Note Series) by Albrecht Pfister | |
Paperback: 188
Pages
(1995-10-27)
list price: US$50.00 -- used & new: US$40.89 (price subject to change: see help) Asin: 0521467551 Canada | United Kingdom | Germany | France | Japan | |
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65. History of Algebraic Geometry by Jean A. Dieudonne | |
Hardcover: 186
Pages
(1985-05-30)
list price: US$132.50 -- used & new: US$132.50 (price subject to change: see help) Asin: 0412993716 Canada | United Kingdom | Germany | France | Japan | |
66. Algebraic Geometry in Coding Theory and Cryptography by Harald Niederreiter, Chaoping Xing | |
Hardcover: 248
Pages
(2009-09-21)
list price: US$45.00 -- used & new: US$36.81 (price subject to change: see help) Asin: 0691102880 Canada | United Kingdom | Germany | France | Japan | |
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67. Arithmetic Algebraic Geometry: Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Trento, Italy, June ... Mathematics / Fondazione C.I.M.E., Firenze) by Jean-Louis Colliot-Thelene, Kazuya Kato, Paul Vojta | |
Paperback: 223
Pages
(1994-12-13)
list price: US$46.00 -- used & new: US$41.16 (price subject to change: see help) Asin: 3540571108 Canada | United Kingdom | Germany | France | Japan | |
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68. Representation Theory and Complex Geometry (Modern Birkhäuser Classics) by Neil Chriss, Victor Ginzburg | |
Paperback: 495
Pages
(2009-12-01)
list price: US$69.95 -- used & new: US$51.20 (price subject to change: see help) Asin: 0817649379 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description The first half of the book fills the gap between the standard knowledge of a beginner in Lie theory and the much wider background needed by the working mathematician. Thus, Chapters 1-3 and 5-6 provide some basics in symplectic geometry, group actions on Kahler manifolds and Borel--Moore homology, geometry of semisimple groups, equivariant algebraic K-theory "from scratch," topology and algebraic geometry of flag varieties and conjugacy classes, respectively. The material covered by Chapters 5 and 6 (as well as most of Chapter 3) has never been presented in book form. Chapters 3-4 and 7-8 form the heart of the book, presenting a uniform approach to representation theory of three quite different objects: (1) Weyl groups; (2) Lie algebra sln; (3) Iwahori--Hecke algebra. The results of Chapters 4 and 8 are new, with complete proofs, not to be found elsewhere in the literature. The techniques developed are quite general and can be successfully applied to such other areas of mathematics, as Quantum groups, affine Lie algebras, and quantum field theory. The exposition is practically self-contained and each chapter potentially serving as a basis for a graduate course. Customer Reviews (1)
a nice blend of mathematics other perspectives in ring theory from a geometricpoint of view (which could serve as yet another compliment) is Broho's 'nilpotent orbits, primitive ideals and characteristic classes' no doubt, the advanced graduate student and professional mathematician would do well in, at least, taking a peek at the contents and theextensive introduction to whet his appetite and peak his curiousity! ... Read more |
69. An Introduction to Algebraic Geometry (Translations of Mathematical Monographs) by Kenji Ueno | |
Paperback: 246
Pages
(1997-06-17)
list price: US$88.00 -- used & new: US$66.40 (price subject to change: see help) Asin: 0821811444 Canada | United Kingdom | Germany | France | Japan | |
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70. A Vector Space Approach to Geometry by Melvin Hausner | |
Paperback: 416
Pages
(2010-07-21)
list price: US$18.95 -- used & new: US$12.89 (price subject to change: see help) Asin: 0486404528 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (7)
Geometric Overview of Core Math and Physics +++
A bit longwinded
Must have if on the road to Linear Algebra
A useful High School Geometry book for Computer Graphics The almost four hundred pages book is remarkably readable and is very consistent at that.There are both worked out examples and exercise problems, for each section - which are very useful for self-study or revision. If you have never had an introduction to linear algebra before, you may have to supplement this with a linear algebra book.But if you have not had a good course in elementary geometry, and your motivation is getting started with elementary Computer Graphics/CAD and the likes, this is a good book for that. Interspersed with the subject matter discussed at a elementary level, in a useful, stimulating style are small, interesting discussions on such useful and relatively advanced topics as function spaces, fixed point theorem in affine transformation, simplices, symmetries etc.I rarely have seen any of these topics mentioned in a book aimed at this level. Highly recommended for freshman undergraduates and those without any mathematics experience who want to start in Graphics, CAD, CAGD and the likes.Recommended also for experienced practitioners in Graphics: it is good to review the fundamentals once in a while, and a well written bookthat is a quick read helps at that!
Perfect for first and second year, or physicists It is a formal math book, with axioms, but it is strong on motivation and has some quite amusing examples. Keywords: tangent spaces, determinants, barycentric, linear transformations. ... Read more |
71. Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups (Lecture Notes in Physics Monographs) by Ludwig Pittner | |
Hardcover: 469
Pages
(1995-12-20)
list price: US$109.00 -- used & new: US$109.00 (price subject to change: see help) Asin: 3540605878 Canada | United Kingdom | Germany | France | Japan | |
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72. Algebraic Geometry: A Volume in Memory of Paolo Francia ([De Gruyter Proceedings in Mathematics]) | |
Hardcover: 355
Pages
(2002-09)
list price: US$217.00 -- used & new: US$128.74 (price subject to change: see help) Asin: 3110171805 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description A part of the articles grew out a Conference in memory of Paolo Francia (1951–2000) held in Genova in September 2001 with about 70 participants. |
73. Koszul Cohomology and Algebraic Geometry (University Lecture Series) by Marian Aprodu and Jan Nagel | |
Paperback: 125
Pages
(2009-12-14)
list price: US$39.00 -- used & new: US$35.14 (price subject to change: see help) Asin: 0821849646 Canada | United Kingdom | Germany | France | Japan | |
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74. An Algebraic Introduction to Complex Projective Geometry: Commutative Algebra (Cambridge Studies in Advanced Mathematics) by Christian Peskine | |
Paperback: 244
Pages
(2009-04-09)
list price: US$48.00 -- used & new: US$38.58 (price subject to change: see help) Asin: 0521108470 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
brief, but good |
75. Algebraic Number Theory and Fermat's Last Theorem: Third Edition by Ian Stewart, David Tall | |
Hardcover: 250
Pages
(2001-12-01)
list price: US$59.00 -- used & new: US$57.13 (price subject to change: see help) Asin: 1568811195 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (7)
Not bad, but much to be improved.
Great Introductory Book to Algebraic Number Theory
skips too much
tough problems => good for the student
Very clear introduction to Algebraic Number Theory |
76. Algebraic Geometry III: Complex Algebraic Varieties. Algebraic Curves and Their Jacobians (Encyclopaedia of Mathematical Sciences) | |
Hardcover: 270
Pages
(1997-12-16)
list price: US$149.00 -- used & new: US$90.46 (price subject to change: see help) Asin: 3540546812 Canada | United Kingdom | Germany | France | Japan | |
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77. Introduction to Commutative Algebra and Algebraic Geometry by Ernst Kunz | |
Hardcover: 256
Pages
(1984-01-01)
list price: US$69.95 -- used & new: US$51.01 (price subject to change: see help) Asin: 0817630651 Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description |
78. Tropical Algebraic Geometry (Oberwolfach Seminars) by Ilia Itenberg, Grigory Mikhalkin, Eugenii I. Shustin | |
Paperback: 104
Pages
(2009-05-28)
list price: US$29.95 -- used & new: US$22.69 (price subject to change: see help) Asin: 303460047X Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description These notes present a polished introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject. It consists of three chapters which complete each other and give a possibility for non-specialists to make the first steps in the subject which is not yet well represented in the literature. The notes are based on a seminar at the Mathematical Research Center in Oberwolfach in October 2004. The intended audience is graduate, post-graduate, and Ph.D. students as well as established researchers in mathematics. |
79. Effective Methods in Algebraic Geometry (Progress in Mathematics) by T. Mora, C. Traverso | |
Hardcover: 514
Pages
(1991-05-01)
list price: US$205.00 -- used & new: US$192.91 (price subject to change: see help) Asin: 0817635467 Canada | United Kingdom | Germany | France | Japan | |
80. Combinatorial Convexity and Algebraic Geometry (Graduate Texts in Mathematics) by Günter Ewald | |
Hardcover: 372
Pages
(1996-10-03)
list price: US$79.95 -- used & new: US$63.56 (price subject to change: see help) Asin: 0387947558 Average Customer Review: Canada | United Kingdom | Germany | France | Japan | |
Editorial Review Product Description Customer Reviews (1)
An excellent way to begin a study of algebraic geometry Loosely speaking, a toric variety is a complex algebraic variety which is the partial compactification of an algebraic torus. The algebraic torus acts on a point in the toric variety such that the orbit of the point is an embedded copy of the algebraic torus. Toric varieties are excellent concrete examples of algebraic varieties since they are characterized entirely by a combinatorial object called its fan, which is a collection of convex cones. This book is an fine introduction to toric varieties. The author does a thorough job of detailing the relevant background in the first half of the book, which deals mostly with convexity and the geometry of lattice polytopes. A very interesting discussion of the Picard group is given in the last few sections of this part. This is one of the best discussions I have seen in the literature on this subject as it gives the reader a very intuitive and concrete view of this group. The second half covers toric varieties in detail with systems of rational functions on a toric variety studied via sheaf theory. The reader familiar with sheaf theory from general algebraic geometry will see it take on a beautifully concrete form in this book. Readers new to algebraic geometry will appreciate the more abstract approach to sheaf theory if they move on to these more advanced treatments. The author gives many examples of the constructions involved with toric varieties. The cohomology of toric varieties is also treated very nicely, and here again, a reader with a modest background in combinatorial topology will follow the presentation. The physicist reader doing research into mirror symmetry will appreciate this book, as toric varieties serve as a good starting point for the constructions in that area. ... Read more |
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