The adjunction theory of complex projective varieties:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin u.a.
de Gruyter
1995
|
| Schriftenreihe: | De Gruyter expositions in mathematics
16 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 398 S. |
| ISBN: | 3110143550 |
Internformat
MARC
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| 100 | 1 | |a Beltrametti, Mauro C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The adjunction theory of complex projective varieties |c by Mauro C. Beltrametti ; Andrew J. Sommese |
| 264 | 1 | |a Berlin u.a. |b de Gruyter |c 1995 | |
| 300 | |a XX, 398 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter expositions in mathematics |v 16 | |
| 650 | 7 | |a Espaces projectifs |2 ram | |
| 650 | 7 | |a Plongements (Mathématiques) |2 ram | |
| 650 | 7 | |a Variétés algébriques |2 ram | |
| 650 | 4 | |a Adjunction theory | |
| 650 | 4 | |a Algebraic varieties | |
| 650 | 4 | |a Embeddings (Mathematics) | |
| 650 | 4 | |a Projective spaces | |
| 650 | 0 | 7 | |a Adjunktion |g Mathematik |0 (DE-588)4373166-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Komplexer projektiver Raum |0 (DE-588)4164906-0 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Sommese, Andrew John |e Verfasser |4 aut | |
| 830 | 0 | |a De Gruyter expositions in mathematics |v 16 |w (DE-604)BV004069300 |9 16 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006598517&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006598517 | ||
Datensatz im Suchindex
| _version_ | 1804124328052129792 |
|---|---|
| adam_text | Contents
Preface vii
List of tables xxi
Chapter 1
General background results 1
1.1 Some basic definitions 1
1.2 Surface singularities 12
1.3 On the singularities that arise in adjunction theory 16
1.4 Curves 21
1.5 Nefvalue results 25
1.6 Universal sections and discriminant varieties 27
1.7 Bertini theorems 34
1.8 Some examples 40
Chapter 2
Consequences of positivity 42
2.1 /t ampleness and A bigness 43
2.2 Vanishing theorems 45
2.3 The Lefschetz hyperplane section theorem 50
2.4 The Albanese mapping in the presence of rational singularities .... 56
2.5 The Hodge index theorem and the Kodaira lemma 58
2.6 Rossi s extension theorems 63
2.7 Theorems of Andreotti Grauert and Griffiths 68
Chapter 3
The basic varieties of adjunction theory 70
3.1 Recognizing projective spaces and quadrics 70
3.2 P^ bundles 73
3.3 Special varieties arising in adjunction theory 80
xviii Contents
Chapter 4
The Hilbert scheme and extremal rays 83
4.1 Flatness, the Hilbert scheme, and limited families 83
4.2 Extremal rays and the cone theorem 90
4.3 Varieties with nonnef canonical bundle 98
Chapter 5
Restrictions imposed by ample divisors 103
5.1 On the behavior of A: big and ample divisors under maps 103
5.2 Extending morphisms of ample divisors 107
5.3 Ample divisors with trivial pluricanonical systems Ill
5.4 Varieties that can be ample divisors only on cones 112
5.5 ¥d bundles as ample divisors 117
Chapter 6
Families of unbreakable rational curves 120
6.1 Examples 121
6.2 Families of unbreakable rational curves 123
6.3 The nonbreaking lemma 126
6.4 Morphisms of varieties covered by unbreakable
rational curves 136
6.5 The classification of projective manifolds covered by lines 144
6.6 Some spannedness results 148
Chapter 7
General adjunction theory 154
7.1 Spectral values 156
7.2 Polarized pairs (M, i£) with nefvalue dim M — 1
and M singular 159
7.3 The first reduction of a singular variety 168
7.4 The polarization of the first reduction 173
7.5 The second reduction in the smooth case 176
7.6 Properties of the first and the second reduction 185
7.7 The second reduction (X, 2s) with Kx + (n 3)9) nef 192
7.8 The three dimensional case 202
7.9 Applications 204
Contents xix
Chapter 8
Background for classical adjunction theory 213
8.1 Numerical implications of nonnegative Kodaira dimension 213
8.2 The double point formula for surfaces 217
8.3 Smooth double covers of irreducible quadric surfaces 217
8.4 Surfaces with one dimensional projection from a line 218
8.5 ft very ampleness 225
8.6 Surfaces with Castelnuovo curves as hyperplane sections 229
8.7 Polarized varieties (X, L) with sectional genus g(L) = h](€x) 234
8.8 Spannedness of Kx + (dim X)L for ample and spanned L 236
8.9 Polarized varieties (X, L) with sectional genus g{L) 1 241
8.10 Classification of varieties up to degree 4 243
Chapter 9
The adjunction mapping 246
9.1 Spannedness of adjoint bundles at singular points 247
9.2 The adjunction mapping 249
Chapter 10
Classical adjunction theory of surfaces 253
10.1 When the adjunction mapping has lower dimensional image 254
10.2 Surfaces with sectional genus g(L) 3 258
10.3 Very ampleness of the adjoint bundle 265
10.4 Very ampleness of the adjoint bundle for degree d 9 265
10.5 Very ampleness of the adjoint bundle when hl{ 8s) 0 270
10.6 Very ampleness of the adjoint bundle when hl(€s) = 0 273
10.7 Preservation of k ery ampleness under adjunction 278
Chapter 11
Classical adjunction theory in dimension 3 280
11.1 Some results on scrolls 281
11.2 The adjunction mapping with a lower dimensional image 284
11.3 Very ampleness of the adjoint bundle 287
11.4 Applications to hyperelliptic curve sections 288
11.5 Projective normality of adjoint bundles 292
11.6 Manifolds of sectional genus 4 294
11.7 The Fano Morin adjunction process 298
xx Contents
Chapter 12
The second reduction in dimension three 302
12.1 Exceptional divisors of the second reduction morphism 303
12.2 The structure of the second reduction 308
12.3 The second reduction for threefolds in P5 314
Chapter 13
Varieties (jM,, X) with k(Km + (dim M 2)56) 0 316
13.1 The double point formula for threefolds 317
13.2 The linear system KM + (n — 2)L on the first reduction (M, L) . . . . 322
13.3 Some Chern inequalities for ample divisors 326
Chapter 14
Special varieties 328
14.1 Structure results for scrolls 329
14.2 Structure results for quadric fibrations 336
14.3 Varieties with small invariants 340
14.4 Projective manifolds with positive defect 346
14.5 Hyperplane sections of curves 351
Bibliography 355
Index 395
|
| any_adam_object | 1 |
| author | Beltrametti, Mauro C. Sommese, Andrew John |
| author_facet | Beltrametti, Mauro C. Sommese, Andrew John |
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| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/5 |
| dewey-search | 516.3/5 |
| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV009956712 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:43:55Z |
| institution | BVB |
| isbn | 3110143550 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006598517 |
| oclc_num | 30895159 |
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| owner_facet | DE-703 DE-739 DE-91G DE-BY-TUM DE-12 DE-29T DE-19 DE-BY-UBM DE-634 DE-11 DE-188 |
| physical | XX, 398 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | de Gruyter |
| record_format | marc |
| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Beltrametti, Mauro C. Verfasser aut The adjunction theory of complex projective varieties by Mauro C. Beltrametti ; Andrew J. Sommese Berlin u.a. de Gruyter 1995 XX, 398 S. txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 16 Espaces projectifs ram Plongements (Mathématiques) ram Variétés algébriques ram Adjunction theory Algebraic varieties Embeddings (Mathematics) Projective spaces Adjunktion Mathematik (DE-588)4373166-1 gnd rswk-swf Komplexer projektiver Raum (DE-588)4164906-0 gnd rswk-swf Projektive Varietät (DE-588)4327070-0 gnd rswk-swf Komplexer projektiver Raum (DE-588)4164906-0 s Projektive Varietät (DE-588)4327070-0 s Adjunktion Mathematik (DE-588)4373166-1 s DE-604 Sommese, Andrew John Verfasser aut De Gruyter expositions in mathematics 16 (DE-604)BV004069300 16 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006598517&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beltrametti, Mauro C. Sommese, Andrew John The adjunction theory of complex projective varieties De Gruyter expositions in mathematics Espaces projectifs ram Plongements (Mathématiques) ram Variétés algébriques ram Adjunction theory Algebraic varieties Embeddings (Mathematics) Projective spaces Adjunktion Mathematik (DE-588)4373166-1 gnd Komplexer projektiver Raum (DE-588)4164906-0 gnd Projektive Varietät (DE-588)4327070-0 gnd |
| subject_GND | (DE-588)4373166-1 (DE-588)4164906-0 (DE-588)4327070-0 |
| title | The adjunction theory of complex projective varieties |
| title_auth | The adjunction theory of complex projective varieties |
| title_exact_search | The adjunction theory of complex projective varieties |
| title_full | The adjunction theory of complex projective varieties by Mauro C. Beltrametti ; Andrew J. Sommese |
| title_fullStr | The adjunction theory of complex projective varieties by Mauro C. Beltrametti ; Andrew J. Sommese |
| title_full_unstemmed | The adjunction theory of complex projective varieties by Mauro C. Beltrametti ; Andrew J. Sommese |
| title_short | The adjunction theory of complex projective varieties |
| title_sort | the adjunction theory of complex projective varieties |
| topic | Espaces projectifs ram Plongements (Mathématiques) ram Variétés algébriques ram Adjunction theory Algebraic varieties Embeddings (Mathematics) Projective spaces Adjunktion Mathematik (DE-588)4373166-1 gnd Komplexer projektiver Raum (DE-588)4164906-0 gnd Projektive Varietät (DE-588)4327070-0 gnd |
| topic_facet | Espaces projectifs Plongements (Mathématiques) Variétés algébriques Adjunction theory Algebraic varieties Embeddings (Mathematics) Projective spaces Adjunktion Mathematik Komplexer projektiver Raum Projektive Varietät |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006598517&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004069300 |
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