On fundamental groups of Galois closures of generic projections:
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Bonn
Math. Inst. der Univ.
2004
|
| Series: | Bonner mathematische Schriften
367 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 89 S. |
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MARC
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Record in the Search Index
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| adam_text | Titel: On fundamental groups of Galois closures of generic projections
Autor: Liedtke, Christian
Jahr: 2004
Contents
Introduction iii
1 A short reminder on fundamental groups 1
1.1 Algebraic curves .......................... 1
1.2 Algebraic surfaces ......................... 1
1.3 Complements of branch divisors.................. 3
2 Generic projections and their Galois closures 5
2.1 Sufficiently ample line bundles................... 5
2.2 Galois closures of generic projections............... 7
2.3 Questions on connectivity...................... 8
3 Semidirect products by symmetric groups 11
3.1 Definition of AC(?, n) and£(?, n)................. 11
3.2 Properties.............................. 13
3.3 Universality............................. 17
3.4 (Counter-)Examples......................... 20
4 A first quotient of 7rx (Xga[) and iri (X|^,) 23
4.1 Etale and topological fundamental groups............. 23
4.2 The quotient for the etale fundamental group............ 25
4.3 Classifying covers with group actions............... 31
4.4 Loops and the orbifold fundamental group............. 37
4.5 The quotient in the topological setup................ 39
5 A generalised symmetric group 43
5.1 Definition of S?(d)......................... 43
5.2 The connection with £(?,n).................... 44
5.3 Afiine subgroups and the construction of K(~,n)......... 50
5.4 Examples.............................. 57
Appendix to Section 5.......................... 58
5.5 Group homology and the computation of Hi............ 58
5.6 Examples from the theory of Coxeter groups............ 60
6 Conclusion 63
6.1 The algorithm of Zariski and van Kampen............. 63
6.2 On the fundamental group of X^{................. 67
6.3 Adding the line at infinity...................... 71
6.4 Generic projections from simply connected surfaces........ 75
6.5 A purely topological description of the Galois closure....... 76
7 Examples 81
7.1 P2.................................. 81
7.2 P1 x P!............................... 81
7.3 Surfaces in P3............................ 82
7.4 Hirzebruch surfaces......................... 82
7.5 Geometrically ruled surfaces.................... 83
7.6 An instructive counter-example................... 84
Notations 86
References 87
|
| adam_txt |
Titel: On fundamental groups of Galois closures of generic projections
Autor: Liedtke, Christian
Jahr: 2004
Contents
Introduction iii
1 A short reminder on fundamental groups 1
1.1 Algebraic curves . 1
1.2 Algebraic surfaces . 1
1.3 Complements of branch divisors. 3
2 Generic projections and their Galois closures 5
2.1 Sufficiently ample line bundles. 5
2.2 Galois closures of generic projections. 7
2.3 Questions on connectivity. 8
3 Semidirect products by symmetric groups 11
3.1 Definition of AC(?, n) and£(?, n). 11
3.2 Properties. 13
3.3 Universality. 17
3.4 (Counter-)Examples. 20
4 A first quotient of 7rx (Xga[) and iri (X|^,) 23
4.1 Etale and topological fundamental groups. 23
4.2 The quotient for the etale fundamental group. 25
4.3 Classifying covers with group actions. 31
4.4 Loops and the orbifold fundamental group. 37
4.5 The quotient in the topological setup. 39
5 A generalised symmetric group 43
5.1 Definition of S?(d). 43
5.2 The connection with £(?,n). 44
5.3 Afiine subgroups and the construction of K(~,n). 50
5.4 Examples. 57
Appendix to Section 5. 58
5.5 Group homology and the computation of Hi. 58
5.6 Examples from the theory of Coxeter groups. 60
6 Conclusion 63
6.1 The algorithm of Zariski and van Kampen. 63
6.2 On the fundamental group of X^{. 67
6.3 Adding the line at infinity. 71
6.4 Generic projections from simply connected surfaces. 75
6.5 A purely topological description of the Galois closure. 76
7 Examples 81
7.1 P2. 81
7.2 P1 x P!. 81
7.3 Surfaces in P3. 82
7.4 Hirzebruch surfaces. 82
7.5 Geometrically ruled surfaces. 83
7.6 An instructive counter-example. 84
Notations 86
References 87 |
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| physical | VIII, 89 S. |
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| publisher | Math. Inst. der Univ. |
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| series | Bonner mathematische Schriften |
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| spelling | Liedtke, Christian 1976- Verfasser (DE-588)137817835 aut On fundamental groups of Galois closures of generic projections von Christian Liedtke Bonn Math. Inst. der Univ. 2004 VIII, 89 S. txt rdacontent n rdamedia nc rdacarrier Bonner mathematische Schriften 367 Bonn, Univ., Diss., 2004 Fundamental groups Galois cohomology Fundamentalgruppe (DE-588)4155638-0 gnd rswk-swf Projektion Mathematik (DE-588)4175877-8 gnd rswk-swf Hüllenoperator (DE-588)4767158-0 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Fundamentalgruppe (DE-588)4155638-0 s Hüllenoperator (DE-588)4767158-0 s Projektion Mathematik (DE-588)4175877-8 s DE-604 Bonner mathematische Schriften 367 (DE-604)BV000001610 367 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014593597&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Liedtke, Christian 1976- On fundamental groups of Galois closures of generic projections Bonner mathematische Schriften Fundamental groups Galois cohomology Fundamentalgruppe (DE-588)4155638-0 gnd Projektion Mathematik (DE-588)4175877-8 gnd Hüllenoperator (DE-588)4767158-0 gnd |
| subject_GND | (DE-588)4155638-0 (DE-588)4175877-8 (DE-588)4767158-0 (DE-588)4113937-9 |
| title | On fundamental groups of Galois closures of generic projections |
| title_auth | On fundamental groups of Galois closures of generic projections |
| title_exact_search | On fundamental groups of Galois closures of generic projections |
| title_exact_search_txtP | On fundamental groups of Galois closures of generic projections |
| title_full | On fundamental groups of Galois closures of generic projections von Christian Liedtke |
| title_fullStr | On fundamental groups of Galois closures of generic projections von Christian Liedtke |
| title_full_unstemmed | On fundamental groups of Galois closures of generic projections von Christian Liedtke |
| title_short | On fundamental groups of Galois closures of generic projections |
| title_sort | on fundamental groups of galois closures of generic projections |
| topic | Fundamental groups Galois cohomology Fundamentalgruppe (DE-588)4155638-0 gnd Projektion Mathematik (DE-588)4175877-8 gnd Hüllenoperator (DE-588)4767158-0 gnd |
| topic_facet | Fundamental groups Galois cohomology Fundamentalgruppe Projektion Mathematik Hüllenoperator Hochschulschrift |
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