Classification theories of polarized varieties:
A polarised variety is a modern generalization of the notion of a variety in classical algebraic geometry. It consists of a pair: the algebraic variety itself, together with an ample line bundle on it. Using techniques from abstract algebraic geometry that have been developed over recent decades, Pr...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1990
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| Schriftenreihe: | London Mathematical Society lecture note series
155 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | A polarised variety is a modern generalization of the notion of a variety in classical algebraic geometry. It consists of a pair: the algebraic variety itself, together with an ample line bundle on it. Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of such pairs using invariants that are polarised higher-dimensional versions of the genus of algebraic curves. The heart of the book is the theory of D-genus and sectional genus developed by the author, but numerous related topics are discussed or surveyed. Proofs are given in full in the central part of the development, but background and technical results are sometimes just sketched when the details are not essential for understanding the key ideas. Readers are assumed to have some background in algebraic geometry, including sheaf cohomology, and for them this work will provide an illustration of the power of modern abstract techniques applied to concrete geometric problems. Thus the book helps the reader not only to understand about classical objects but also modern methods, and so it will be useful not only for experts but also non-specialists and graduate students |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xiv, 205 pages) |
| ISBN: | 9780511662638 |
| DOI: | 10.1017/CBO9780511662638 |
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| 520 | |a A polarised variety is a modern generalization of the notion of a variety in classical algebraic geometry. It consists of a pair: the algebraic variety itself, together with an ample line bundle on it. Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of such pairs using invariants that are polarised higher-dimensional versions of the genus of algebraic curves. The heart of the book is the theory of D-genus and sectional genus developed by the author, but numerous related topics are discussed or surveyed. Proofs are given in full in the central part of the development, but background and technical results are sometimes just sketched when the details are not essential for understanding the key ideas. Readers are assumed to have some background in algebraic geometry, including sheaf cohomology, and for them this work will provide an illustration of the power of modern abstract techniques applied to concrete geometric problems. Thus the book helps the reader not only to understand about classical objects but also modern methods, and so it will be useful not only for experts but also non-specialists and graduate students | ||
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Datensatz im Suchindex
| _version_ | 1804176885016428544 |
|---|---|
| any_adam_object | |
| author | Fujita, Takao |
| author_facet | Fujita, Takao |
| author_role | aut |
| author_sort | Fujita, Takao |
| author_variant | t f tf |
| building | Verbundindex |
| bvnumber | BV043942338 |
| classification_rvk | SI 320 SK 240 |
| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9780511662638 (OCoLC)849791727 (DE-599)BVBBV043942338 |
| dewey-full | 516.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.353 |
| dewey-search | 516.353 |
| dewey-sort | 3516.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511662638 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511662638 |
| language | English |
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| publisher | Cambridge University Press |
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| spelling | Fujita, Takao Verfasser aut Classification theories of polarized varieties Takao Fujita Cambridge Cambridge University Press 1990 1 online resource (xiv, 205 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 155 Title from publisher's bibliographic system (viewed on 05 Oct 2015) A polarised variety is a modern generalization of the notion of a variety in classical algebraic geometry. It consists of a pair: the algebraic variety itself, together with an ample line bundle on it. Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of such pairs using invariants that are polarised higher-dimensional versions of the genus of algebraic curves. The heart of the book is the theory of D-genus and sectional genus developed by the author, but numerous related topics are discussed or surveyed. Proofs are given in full in the central part of the development, but background and technical results are sometimes just sketched when the details are not essential for understanding the key ideas. Readers are assumed to have some background in algebraic geometry, including sheaf cohomology, and for them this work will provide an illustration of the power of modern abstract techniques applied to concrete geometric problems. Thus the book helps the reader not only to understand about classical objects but also modern methods, and so it will be useful not only for experts but also non-specialists and graduate students Algebraic varieties / Classification theory Polarisierte Mannigfaltigkeit (DE-588)4248078-4 gnd rswk-swf Klassifikationstheorie (DE-588)4164034-2 gnd rswk-swf Projektive Mannigfaltigkeit (DE-588)4175888-2 gnd rswk-swf Klassifikation (DE-588)4030958-7 gnd rswk-swf Projektive Mannigfaltigkeit (DE-588)4175888-2 s Klassifikationstheorie (DE-588)4164034-2 s 1\p DE-604 Polarisierte Mannigfaltigkeit (DE-588)4248078-4 s Klassifikation (DE-588)4030958-7 s 2\p DE-604 Erscheint auch als Druckausgabe 978-0-521-39202-0 https://doi.org/10.1017/CBO9780511662638 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fujita, Takao Classification theories of polarized varieties Algebraic varieties / Classification theory Polarisierte Mannigfaltigkeit (DE-588)4248078-4 gnd Klassifikationstheorie (DE-588)4164034-2 gnd Projektive Mannigfaltigkeit (DE-588)4175888-2 gnd Klassifikation (DE-588)4030958-7 gnd |
| subject_GND | (DE-588)4248078-4 (DE-588)4164034-2 (DE-588)4175888-2 (DE-588)4030958-7 |
| title | Classification theories of polarized varieties |
| title_auth | Classification theories of polarized varieties |
| title_exact_search | Classification theories of polarized varieties |
| title_full | Classification theories of polarized varieties Takao Fujita |
| title_fullStr | Classification theories of polarized varieties Takao Fujita |
| title_full_unstemmed | Classification theories of polarized varieties Takao Fujita |
| title_short | Classification theories of polarized varieties |
| title_sort | classification theories of polarized varieties |
| topic | Algebraic varieties / Classification theory Polarisierte Mannigfaltigkeit (DE-588)4248078-4 gnd Klassifikationstheorie (DE-588)4164034-2 gnd Projektive Mannigfaltigkeit (DE-588)4175888-2 gnd Klassifikation (DE-588)4030958-7 gnd |
| topic_facet | Algebraic varieties / Classification theory Polarisierte Mannigfaltigkeit Klassifikationstheorie Projektive Mannigfaltigkeit Klassifikation |
| url | https://doi.org/10.1017/CBO9780511662638 |
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