Higher dimensional varieties and rational points:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer [u.a.]
2003
|
| Series: | Bolyai Society mathematical studies
12 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 310 S. graph. Darst. |
| ISBN: | 3540008209 9639453021 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Contents 3
Introduction 7
Acknowledgments 9
PART I: GEOMETRY
Carolina Araujo and Janos Kollar, Rational Curves on
Varieties 13
1. Rational curves on surfaces 13
2. Deformation of morphisms I 17
3. Deforming rational curves 19
4. Deformation of morphisms II 23
5. Deforming nonfree rational curves I 28
6. Deforming nonfree rational curves II 31
7. Rationally connected varieties 35
8. Genus zero stable curves 44
9. Finding rational curves over nonclosed fields 48
10. Moduli spaces of stable curves 53
Janos Kollar, Rationally Connected Varieties and Fundamental
Groups 69
1. Statements of the main results 71
2. Fundamental groups in families 73
3. Proofs of the theorems 78
4. Applications to non closed fields 88
Olivier Debarre, Fano Varieties 93
1. Definitions and examples 93
2. Toric Fano varieties 96
3. Rational curves on smooth Fano varieties Ill
4. The differential geometric point of view 123
5. Simple connectedness of complex Fano varieties 124
SANDOR J. KOVACS, Families of Varieties of General Type: the
Shafarevich Conjecture and Related Problems 133
1. The function field case 136
2. The number field case 139
3. Hyperbolicity 141
4. Vanishing theorems 143
5. Families of curves 144
6. Moduli spaces of curves 145
7. Boundedness 148
8. Hyperbolicity revisited 150
9. Weak boundedness 150
10. Higher dimensional fibers 152
11. Positivity of push forwards 154
12. Logarithmic vanishing theorems 156
13. Smooth fibers that are minimal of general type and singular
fibers 157
14. Higher dimensional bases 162
PART II: ARITHMETIC
Jean Louis Colliot Thelene, Points rationnels sur les fibrations . 171
1. La descente ouverte 177
2. Pinceaux d espaces homogenes de varietes abeliennes 189
3. Surfaces et hypersurfaces cubiques diagonales sur un corps de
fonctions 204
Brendan Hassett. Potential Density of Rational Points on
Algebraic: Varieties 223
1. Introduction 223
2. The notion of potential density 225
3. Basic properties of potential density 226
4. Abelian fibrations 229
5. Fano varieties 234
6. K3 surfaces 235
7. Twisting elliptic fibrations 242
8. Approach I: Irreducibility of torsion in the nonisotrivial case 248
9. Approach II: Genus estimates 254
10. Approach III: Elliptic multisections (based on correspondence
with J. Kollar) 266
11. Symmetric products of K3 surfaces 273
Appendix: Galois cohoinology and principal homogeneous spaces 276
Yuri Tschinkel, Fujita s Program and Rational Points 283
1. Introduction 283
2. Geometry 285
3. Arithmetic 291
4. Tamagawa numbers 294
5. Analysis 300
|
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| ctrlnum | (OCoLC)52203059 (DE-599)BVBBV016995234 |
| dewey-full | 516.3/53 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-tens | 510 - Mathematics |
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| genre_facet | Konferenzschrift 2001 Budapest |
| id | DE-604.BV016995234 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:12:33Z |
| institution | BVB |
| isbn | 3540008209 9639453021 |
| language | English |
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| physical | 310 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer [u.a.] |
| record_format | marc |
| series | Bolyai Society mathematical studies |
| series2 | Bolyai Society mathematical studies |
| spelling | Higher dimensional varieties and rational points Károly Böröczky ... (eds.) Berlin [u.a.] Springer [u.a.] 2003 310 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bolyai Society mathematical studies 12 Algebraic varieties Rational points (Geometry) Algebraische Varietät (DE-588)4581715-7 gnd rswk-swf Rationaler Punkt (DE-588)4177004-3 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2001 Budapest gnd-content Algebraische Varietät (DE-588)4581715-7 s Rationaler Punkt (DE-588)4177004-3 s DE-604 Böröczky, Károly Sonstige oth Bolyai Society mathematical studies 12 (DE-604)BV010908507 12 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010258861&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Higher dimensional varieties and rational points Bolyai Society mathematical studies Algebraic varieties Rational points (Geometry) Algebraische Varietät (DE-588)4581715-7 gnd Rationaler Punkt (DE-588)4177004-3 gnd |
| subject_GND | (DE-588)4581715-7 (DE-588)4177004-3 (DE-588)1071861417 |
| title | Higher dimensional varieties and rational points |
| title_auth | Higher dimensional varieties and rational points |
| title_exact_search | Higher dimensional varieties and rational points |
| title_full | Higher dimensional varieties and rational points Károly Böröczky ... (eds.) |
| title_fullStr | Higher dimensional varieties and rational points Károly Böröczky ... (eds.) |
| title_full_unstemmed | Higher dimensional varieties and rational points Károly Böröczky ... (eds.) |
| title_short | Higher dimensional varieties and rational points |
| title_sort | higher dimensional varieties and rational points |
| topic | Algebraic varieties Rational points (Geometry) Algebraische Varietät (DE-588)4581715-7 gnd Rationaler Punkt (DE-588)4177004-3 gnd |
| topic_facet | Algebraic varieties Rational points (Geometry) Algebraische Varietät Rationaler Punkt Konferenzschrift 2001 Budapest |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010258861&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010908507 |
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