Projective Geometry and Formal Geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2004
|
| Schriftenreihe: | Monografie Matematyczne, Instytut Matematyczny Polskiej Akademii Nauk (IMPAN)
65 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XIV, 214 p) |
| ISBN: | 9783034879361 9783034896269 |
| DOI: | 10.1007/978-3-0348-7936-1 |
Internformat
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Datensatz im Suchindex
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| author | Bădescu, Lucian |
| author_facet | Bădescu, Lucian |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-7936-1 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034879361 9783034896269 |
| language | English |
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| series2 | Monografie Matematyczne, Instytut Matematyczny Polskiej Akademii Nauk (IMPAN) |
| spelling | Bădescu, Lucian Verfasser aut Projective Geometry and Formal Geometry by Lucian Bădescu Basel Birkhäuser Basel 2004 1 Online-Ressource (XIV, 214 p) txt rdacontent c rdamedia cr rdacarrier Monografie Matematyczne, Instytut Matematyczny Polskiej Akademii Nauk (IMPAN) 65 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 Mathematics Geometry, algebraic Functions of complex variables Global analysis Geometry Algebraic Geometry Functions of a Complex Variable Global Analysis and Analysis on Manifolds Mathematik Projektive Geometrie (DE-588)4047436-7 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s Projektive Geometrie (DE-588)4047436-7 s 1\p DE-604 https://doi.org/10.1007/978-3-0348-7936-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bădescu, Lucian Projective Geometry and Formal Geometry Mathematics Geometry, algebraic Functions of complex variables Global analysis Geometry Algebraic Geometry Functions of a Complex Variable Global Analysis and Analysis on Manifolds Mathematik Projektive Geometrie (DE-588)4047436-7 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4047436-7 (DE-588)4001161-6 |
| title | Projective Geometry and Formal Geometry |
| title_auth | Projective Geometry and Formal Geometry |
| title_exact_search | Projective Geometry and Formal Geometry |
| title_full | Projective Geometry and Formal Geometry by Lucian Bădescu |
| title_fullStr | Projective Geometry and Formal Geometry by Lucian Bădescu |
| title_full_unstemmed | Projective Geometry and Formal Geometry by Lucian Bădescu |
| title_short | Projective Geometry and Formal Geometry |
| title_sort | projective geometry and formal geometry |
| topic | Mathematics Geometry, algebraic Functions of complex variables Global analysis Geometry Algebraic Geometry Functions of a Complex Variable Global Analysis and Analysis on Manifolds Mathematik Projektive Geometrie (DE-588)4047436-7 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Mathematics Geometry, algebraic Functions of complex variables Global analysis Geometry Algebraic Geometry Functions of a Complex Variable Global Analysis and Analysis on Manifolds Mathematik Projektive Geometrie Algebraische Geometrie |
| url | https://doi.org/10.1007/978-3-0348-7936-1 |
| work_keys_str_mv | AT badesculucian projectivegeometryandformalgeometry |