Name: projective geometry and formal geometry (in English)
Price: 104.20 USD
Availability: InStock
Author: badescu
ISBN: 9783764371234

portada projective geometry and formal geometry (in English)

Type

Physical Book

Publisher

springer publishing map

Author

badescu

Language

English

Pages

209

ISBN

3764371234

ISBN13

9783764371234

Synopsis "projective geometry and formal geometry (in English)"

the aim of this monograph is to introduce the reader to modern methods of projective geometry involving certain techniques of formal geometry. some of these methods are illustrated in the first part through the proofs of a number of results of a rather classical flavor, involving in a crucial way the first infinitesimal neighbourhood of a given subvariety in an ambient variety. motivated by the first part, in the second formal functions on the formal completion x/y of x along a closed subvariety y are studied, particularly the extension problem of formal functions to rational functions. the formal scheme x/y, introduced to algebraic geometry by zariski and grothendieck in the 1950s, is an analogue of the concept of a tubular neighbourhood of a submanifold of a complex manifold. it is very well suited to study the given embedding ysubset x. the deep relationship of formal geometry with the most important connectivity theorems in algebraic geometry, or with complex geometry, is also studied. some of the formal methods are illustrated and applied to homogeneous spaces.the book contains a lot of results obtained over the last thirty years, many of which never appeared in a monograph or textbook. it addresses to algebraic geometers as well as to those interested in using methods of algebraic geometry.