Principles of Algebraic Geometry

Principles of Algebraic Geometry


  • Author : Phillip Griffiths
  • Publisher : John Wiley & Sons
  • Release Date : 2014-08-21
  • Genre: Mathematics
  • Pages :
  • ISBN 10 : 9781118626320


Principles of Algebraic Geometry Book Description :

A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special topics in complex manifolds....

Principles of Algebraic Geometry

Principles of Algebraic Geometry


  • Author : Phillip Griffiths
  • Publisher : John Wiley & Sons
  • Release Date : 2011-08-10
  • Genre: Mathematics
  • Pages :
  • ISBN 10 : 9781118030776


Principles of Algebraic Geometry Book Description :

A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special topics in complex manifolds....

An Invitation to Algebraic Geometry

An Invitation to Algebraic Geometry


  • Author : Karen E. Smith
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-03-09
  • Genre: Mathematics
  • Pages :
  • ISBN 10 : 9781475744972


An Invitation to Algebraic Geometry Book Description :

This is a description of the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra....

Algebraic Geometry and Commutative Algebra
Score: 4
From 1 Ratings

Algebraic Geometry and Commutative Algebra


  • Author : Siegfried Bosch
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-11-15
  • Genre: Mathematics
  • Pages :
  • ISBN 10 : 9781447148296


Algebraic Geometry and Commutative Algebra Book Description :

Algebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry, like algebraic number theory. The new techniques paved the way to spectacular progress such as the proof of Fermat’s Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts. More advanced readers can use the book to broaden their view on the subject. A separate part deals with the necessary prerequisites from co...

An Introduction to Algebraic Geometry and Algebraic Groups

An Introduction to Algebraic Geometry and Algebraic Groups


  • Author : Meinolf Geck
  • Publisher : Clarendon Press
  • Release Date : 2013-03-14
  • Genre: Mathematics
  • Pages :
  • ISBN 10 : 9780191663727


An Introduction to Algebraic Geometry and Algebraic Groups Book Description :

An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles. Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type. The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, a thorough treatment of Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finit...

Algebraic Geometry
Score: 5
From 1 Ratings

Algebraic Geometry


  • Author : Daniel Perrin
  • Publisher : Springer Science & Business Media
  • Release Date : 2007-12-16
  • Genre: Mathematics
  • Pages :
  • ISBN 10 : 1848000561


Algebraic Geometry Book Description :

Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject; it assumes only the standard background of undergraduate algebra. The book starts with easily-formulated problems with non-trivial solutions and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study....

Basic Algebraic Geometry 1

Basic Algebraic Geometry 1


  • Author : Igor R. Shafarevich
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-11-27
  • Genre: Mathematics
  • Pages :
  • ISBN 10 : 9783642579080


Basic Algebraic Geometry 1 Book Description :

This book is a revised and expanded new edition of the first four chapters of Shafarevich’s well-known introductory book on algebraic geometry. Besides correcting misprints and inaccuracies, the author has added plenty of new material, mostly concrete geometrical material such as Grassmannian varieties, plane cubic curves, the cubic surface, degenerations of quadrics and elliptic curves, the Bertini theorems, and normal surface singularities....

Complex Geometry

Complex Geometry


  • Author : Daniel Huybrechts
  • Publisher : Springer Science & Business Media
  • Release Date : 2006-03-30
  • Genre: Mathematics
  • Pages :
  • ISBN 10 : 9783540266877


Complex Geometry Book Description :

Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)...

Algebraic Geometry and Arithmetic Curves

Algebraic Geometry and Arithmetic Curves


  • Author : Qing Liu
  • Publisher : Oxford University Press
  • Release Date : 2006-06-29
  • Genre: Mathematics
  • Pages :
  • ISBN 10 : 9780191547805


Algebraic Geometry and Arithmetic Curves Book Description :

This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with ...