Local Analytic Geometry

By: Shreeram Shankar Abhyankar

Write A Review

Hardcover | 16 January 2001

At a Glance

Hardcover
504 Pages

Edition Type
New edition

Dimensions(cm)
21.59 x 15.88 x 3.18

Get Free Shipping

Add this title and get FREE SHIPPING on your whole order*

View Promotion >

FREE SHIPPING

Hardcover

RRP $325.99

$293.50

10%OFF

or 4 interest-free payments of $73.38 with

or

Aims to ship in 30 to 35 business days

This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: algebraic treatment of several complex variables; geometric approach to algebraic geometry via analytic sets; survey of local algebra; and survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from number theory. When it is specialized to the complex case, connectivity and other topological properties come to the fore. In particular, via singularities of analytic sets, topological fundamental groups can be studied. In the transition from punctual to local, ie. from properties at a point to properties near a point, the classical work of Osgood plays an important role. This gives rise to normic forms and the concept of the Osgoodian. Following Serre, the passage from local to global properties of analytic spaces is facilitated by introducing sheaf theory. Here the fundamental results are the coherence theorems of Oka and Cartan. They are followed by theory normalization due to Oka and Zariski in the analytic and algebraic cases, respectively.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Analytic Geometry

Make - Trigonometry

Build your way from triangles to analytic geometry

Paperback

RRP $57.00

$36.90

35%
OFF

FREE SHIPPING

Birth Of China Seen Through Poetry, The

Paperback

RRP $39.99

$35.95

10%
OFF

Geometry Workbook For Dummies

Paperback

RRP $41.95

$33.25

21%
OFF

Convexity from the Geometric Point of View : Cornerstones - Vitor Balestro

$159.40

10%
OFF

Solitons, Instantons, and Twistors : Oxford Graduate Texts in Mathematics - Maciej Dunajski

$86.95

13%
OFF

FREE SHIPPING

A Mathematician and His Mathematical Work - Selected Papers of S. S. Chern

World Scientific Series in 20th Century Mathematics

Hardcover

RRP $469.99

$422.95

10%
OFF

FREE SHIPPING

Two Reports on Harmonic Maps

Hardcover

RRP $178.99

$161.25

10%
OFF

Totally Convex Functions for Fixed Points Computation : Applied Optimization - D. Butnariu

$24.90

17%
OFF

Algebraic Varieties

London Mathematical Society Lecture Note

Paperback

RRP $99.95

$84.95

15%
OFF

FREE SHIPPING

Almost Complex And Complex Structures

SERIES IN PURE MATHEMATICS

Hardcover

RRP $212.99

$191.75

10%
OFF

Analysis and Geometry on Groups

Cambridge Tracts in Mathematics

Hardcover

RRP $203.95

$160.75

21%
OFF

Complex Algebraic Curves

London Mathematical Society Student Texts

Paperback

RRP $91.95

$79.40

14%
OFF

Diagram Geometries

Oxford Science Publications

Hardcover

RRP $454.00

$291.80

36%
OFF

Differential Geometry and Statistics

Monographs on Statistics and Applied Probability

Hardcover

RRP $368.00

$283.80

23%
OFF

FREE SHIPPING

Geometry, Analysis and Mechanics

Hardcover

RRP $277.99

$250.25

10%
OFF

Projective Modules and Complete Intersections : Lecture Notes in Mathematics - Satya Mandal

$24.40

26%
OFF

FREE SHIPPING

Mathematical Methods For System Theory

Hardcover

RRP $243.99

$219.75

10%
OFF

Preface
Instructions to the Reader
Elementary Theory in C[superscript n]
Notation and Terminology	p. 1
Convergent Power Series	p. 6
Laurent Series	p. 17
Cauchy Theory	p. 23
Convexity in R[superscript n]	p. 35
Laurent Expansion in C[superscript n]	p. 48
Domains of Holomorphy	p. 55
A Theorem of Rado	p. 59
Comments on Totally Disconnected Fields	p. 65
Weierstrass Preparation Theorem
Weierstrass Preparation Theorem. Identity Theorem, Finite Ideal Bases and Unique Factorization in Power Series Rings. Implicit Function Theorem	p. 71
Continuity of Roots and Open Map Theorem	p. 90
Hensel's Lemma. Continuity of Algebroid Functions	p. 93
Complex Weierstrass Preparation Theorem	p. 100
Riemann Extension Theorem and Connectivity of Algebroid Hypersurface	p. 107
Oka Coherence	p. 117
Cartan Module Bases	p. 125
Review from Local Algebra
Depth, Height, and Dimension, Completions. Direct Sums Resultants and Discriminants	p. 141
Quotient Rings	p. 149
Integral Dependence and Finite Generation	p. 158
Henselian Rings	p. 173
Order and Rank in Local Rings. Regular Local Rings	p. 178
Another Proof that a Formal Power Series Rings in Noetherian	p. 184
Parameters in Power Series Rings
Parameters for Ideals	p. 189
Perfect Fields	p. 198
Regularity of Quotient Rings	p. 204
Translates of Ideals	p. 211
Dimension of an Intersection	p. 215
Algebraic Lemmas on Algebroid Functions	p. 223
Analytic Sets
The Language of Germs	p. 230
Decomposition of an Analytic Set Germ	p. 233
Ruckert-Weierstrass Parametrization of an Irreducible Analytic Set Germ	p. 246
Ruckert-Weierstrass Parametrization of an Irreducible Analytic Set Germ (Summary)	p. 264
Local Properties of Analytic Sets	p. 271
Connectivity Properties of Complex Analytic Sets	p. 289
Parametrization of a Pure Dimensional Analytic Set	p. 305
Normal Points of Complex Analytic Sets. Remarks on Algebraic Varieties	p. 323
Remmert-Stein-Thullen Theorem on Essential Singularities of Complex Analytic Sets. Theorem of Chow	p. 333
Topological Dimension	p. 346
Remarks on the Fundamental Group	p. 349
Language of Sheaves
Inductive Systems and Presheaves	p. 357
Sheaves	p. 369
Coherent Sheaves	p. 384
Analytic Spaces
Definitions	p. 394
Recapitulation of Properties of Analytic Spaces	p. 402
Invariance of Order and Rank	p. 424
Bimeromorphic Maps and Normalizations	p. 442
Bibliography	p. 471
Index of Notation	p. 475
Subject Index	p. 479
Table of Contents provided by Blackwell. All Rights Reserved.

Local Analytic Geometry

At a Glance

Get Free Shipping

Add this title and get FREE SHIPPING on your whole order* .product-campaign-end-date{display: none !important;}

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Analytic Geometry

Make - Trigonometry

Build your way from triangles to analytic geometry

Birth Of China Seen Through Poetry, The

Geometry Workbook For Dummies

Convexity from the Geometric Point of View

Cornerstones

Fractional Integrals, Potentials, and Radon Transforms

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Circles, Spheres and Spherical Geometry

Birkhauser Advanced Texts / Basler Lehrbucher

Liberty's Grid

A Founding Father, a Mathematical Dreamland, and the Shaping of America

A Journey Through the Wonders of Plane Geometry

Solitons, Instantons, and Twistors

Oxford Graduate Texts in Mathematics

Lines of Development

Analysis, Geometry, Architecture

A Mathematician and His Mathematical Work - Selected Papers of S. S. Chern

World Scientific Series in 20th Century Mathematics

Two Reports on Harmonic Maps

Totally Convex Functions for Fixed Points Computation

Applied Optimization

The Wonder Book of Geometry

A Mathematical Story

Algebraic Varieties

London Mathematical Society Lecture Note

Almost Complex And Complex Structures

SERIES IN PURE MATHEMATICS

Analysis and Geometry on Groups

Cambridge Tracts in Mathematics

Complex Algebraic Curves

London Mathematical Society Student Texts

Diagram Geometries

Oxford Science Publications

Differential Geometry and Statistics

Monographs on Statistics and Applied Probability

Geometry, Analysis and Mechanics

Projective Modules and Complete Intersections

Lecture Notes in Mathematics

Bob Miller's Calc for the Clueless

Calc I

Mathematical Methods For System Theory

This product is categorised by

Popular Searches

Add this title and get FREE SHIPPING on your whole order*