Overview
- Contains results obtained over the last thirty years; many of them were only be published in scientific journals
Part of the book series: Monografie Matematyczne (MONOGRAFIE, volume 65)
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Table of contents (14 chapters)
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Front Matter
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Special Chapters of Projective Geometry
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Front Matter
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Formal Functions in Algebraic Geometry
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Front Matter
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Back Matter
Keywords
About this book
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 Y\subset 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.
Authors and Affiliations
Bibliographic Information
Book Title: Projective Geometry and Formal Geometry
Authors: Lucian Bădescu
Series Title: Monografie Matematyczne
DOI: https://doi.org/10.1007/978-3-0348-7936-1
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: Springer Basel AG 2004
Hardcover ISBN: 978-3-7643-7123-4Published: 25 October 2004
Softcover ISBN: 978-3-0348-9626-9Published: 24 October 2012
eBook ISBN: 978-3-0348-7936-1Published: 06 December 2012
Series ISSN: 0077-0507
Series E-ISSN: 2297-0274
Edition Number: 1
Number of Pages: XIV, 214
Topics: Algebraic Geometry, Functions of a Complex Variable, Global Analysis and Analysis on Manifolds, Geometry