Projective Geometry and Formal Geometry / by Lucian Bădescu
(Monografie Matematyczne, Instytut Matematyczny Polskiej Akademii Nauk (IMPAN) ; 65)
| データ種別 | 電子ブック |
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| 出版情報 | Basel : Birkhäuser Basel : Imprint: Birkhäuser , 2004 |
| 本文言語 | 英語 |
| 大きさ | XIV, 214 p : online resource |
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| 内容注記 | I Special Chapters of Projective Geometry 1 Extensions of Projective Varieties 2 Proof of Theorem 1.3 3 Counterexamples and Further Consequences 4 The Zak Map of a Curve. Gaussian Maps 5 Quasi-homogeneous Singularities and Projective Geometry 6 A Characterization of Linear Subspaces 7 Cohomological Dimension and Connectedness Theorems 8 A Problem of Complete Intersection II Formal Functions in Algebraic Geometry 9 Basic Definitions and Results 10 Lefschetz Theory and Meromorphic Functions 11 Connectedness and Formal Functions 12 Further Results on Formal Functions 13 Formal Functions on Homogeneous Spaces 14 Quasi-lines on Projective Manifolds Glossary of Notation |
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| 一般注記 | 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 |
| 著者標目 | *Bădescu, Lucian author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Algebraic geometry LCSH:Functions of complex variables LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Geometry FREE:Mathematics FREE:Algebraic Geometry FREE:Functions of a Complex Variable FREE:Global Analysis and Analysis on Manifolds FREE:Geometry |
| 分 類 | DC23:516.35 |
| 巻冊次 | ISBN:9783034879361 
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| ISBN | 9783034879361 |
| URL | http://dx.doi.org/10.1007/978-3-0348-7936-1 |
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