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Field name	Details
Dewey Class	516
Title	Local Analytic Geometry ([EBook] :) : Basic Theory and Applications / / by Theo de Jong, Gerhard Pfister.
Author	Jong, Theo de
Added Personal Name	Pfister, Gerhard author.
Other name(s)	SpringerLink (Online service)
Publication	Wiesbaden : : Vieweg+Teubner Verlag : : Imprint: Vieweg+Teubner Verlag, , 2000.
Physical Details	XI, 384 p. 12 illus. : online resource.
Series	Advanced lectures in mathematics 0932-7134
ISBN	9783322901590
Summary Note	Algebraic geometry is, loosely speaking, concerned with the study of zero sets of polynomials (over an algebraically closed field). As one often reads in prefaces of int- ductory books on algebraic geometry, it is not so easy to develop the basics of algebraic geometry without a proper knowledge of commutative algebra. On the other hand, the commutative algebra one needs is quite difficult to understand without the geometric motivation from which it has often developed. Local analytic geometry is concerned with germs of zero sets of analytic functions, that is, the study of such sets in the neighborhood of a point. It is not too big a surprise that the basic theory of local analytic geometry is, in many respects, similar to the basic theory of algebraic geometry. It would, therefore, appear to be a sensible idea to develop the two theories simultaneously. This, in fact, is not what we will do in this book, as the "commutative algebra" one needs in local analytic geometry is somewhat more difficult: one has to cope with convergence questions. The most prominent and important example is the substitution of division with remainder. Its substitution in local analytic geometry is called the Weierstraft Division Theorem. The above remarks motivated us to organize the first four chapters of this book as follows. In Chapter 1 we discuss the algebra we need. Here, we assume the reader attended courses on linear algebra and abstract algebra, including some Galois theory.:
Contents note	1 Algebra -- 2 Affine Algebraic Geometry -- 3 Basics of Analytic Geometry -- 4 Further Development of Analytic Geometry -- 5 Plane Curve Singularities -- 6 The Principle of Conservation of Number -- 7 Standard Bases -- 8 Approximation Theorems -- 9 Classification of Simple Hypersurface Singularities -- 10 Deformations of Singularities.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-322-90159-0
Links to Related Works	Subject References: Geometry . Mathematics . Mathematics, general . Authors: Jong, Theo de . Pfister, Gerhard . Corporate Authors: SpringerLink (Online service) . Series: Advanced lectures in mathematics . Classification: 516 .

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Local Analytic Geometry: Basic Theory and Applications /

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