Configuration spaces over Hilbert schemes and applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
1996
|
| Series: | Lecture notes in mathematics
1647 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 143 S. graph. Darst. |
| ISBN: | 3540620508 |
Staff View
MARC
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| 100 | 1 | |a Dias, Danielle |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Configuration spaces over Hilbert schemes and applications |c Danielle Dias ; Patrick LeBarz |
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Record in the Search Index
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| adam_text | Table of Contents
Introduction
Part one : Double and triple points formula 9
1 Conventions and notation 11
1.1 Fundamental facts 11
1.2 Conventions 11
1.3 Notation 12
2 Double formula 13
2.1 The class of H X) in H^[Z) 13
2.2 Definition of the double class 16
2.3 Computation of the double class 18
2.3.1 Computation of M2 18
2.3.2 19
2.3.3 20
3 Triple formula 22
3.1 The class of H^{~X) in HH~Z) 22
3.2 The triple formula 26
3.2.1 Some notation 26
3.2.2 Computation of M3 and ^.A/3 28
3.2.3 Computation of pri,uTui/i 31
3.2.4 Computation of {s(U) x cW}m 32
3.2.5 Computation of prLWi.i/2, first part 35
3.2.6 Computation of prj.Jl.i/2, second part 38
3.2.7 Conclusion 42
4 Intermediate computations 44
4.1 44
4.2 Flatness of tti and 7T2 44
vi
4.3 Proof of lemma 4.(in) and of U],]H = 0 45
4.4 Proof of lemma 4.(in) 46
4.5 Proof of lemma 4.(u) and (v) 47
4.6 Proof of lemma 1 48
4.7 Flatness of P12 and of P3 49
4.8 Proof of lemma 4.(i) 51
4.9 Proof of lemma 3 52
4.10 Transversality of (3 and 1 53
5 Application to the case where V is a surface and W a volume 55
5.1 Computation of cv(v) 56
5.2 Computation of ci/(w) j 59
5.3 Computation of the contribution of / 63
Part two : Construction of a complete quadruples variety 65
6 Construction of the variety B(V) 67
6.1 Statement of the theorem 67
6.2 Definitions, drawing conventions 67
6.3 Irreducibility and dimension of B(V) 68
6.3.1 General facts on Hilbert schemes : 68
6.3.2 69
6.4 Non singularity of B(V) 77
6.4.0 Preliminaries 78
6.4.1 Non singularity of B(V) at qo where qo is a locally complete
intersection quadruple point 83
6.4.2 Non singularity of B(V) at q0 where q0 is a non locally complete
intersection quadruple point 91
7 Construction of the variety H*{V) 102
7.1 Non singularity of H4(V) at q where q is a locally complete intersection
quadruplet 104
7.1.1 Case of the curvilinear quadruplet 104
7.1.2 Case of the square quadruplet 108
7.2 The variety i/4(V) at q where q is a non locally complete intersection
quadruplet Ill
7.2.1 Case of the elongated quadruplet Ill
7.2.2 Case of the spherical quadruplet 123
7.3 Irreducibility of H V) 127
vii
Appendix A 129
A.I Local chart of H3(V) at t, where t is a curvilinear triple point 129
A.2 Local chart of H3(V) at t, where t is amorphous 130
Appendix B 132
B.I Local chart of H4(V) at an elongated quadruplet 133
B.2 Local equations of HA(y) at a spherical quadruplet 134
Bibliography 136
Index 139
Index of notation 141
|
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:03:28Z |
| institution | BVB |
| isbn | 3540620508 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007413700 |
| oclc_num | 246274961 |
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| physical | VII, 143 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Dias, Danielle Verfasser aut Configuration spaces over Hilbert schemes and applications Danielle Dias ; Patrick LeBarz Berlin [u.a.] Springer 1996 VII, 143 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1647 Hilbert schemes Intersection theory Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Hilbertsches Schema (DE-588)4159868-4 gnd rswk-swf Konfigurationsraum (DE-588)4199256-8 gnd rswk-swf Hilbertsches Schema (DE-588)4159868-4 s Konfigurationsraum (DE-588)4199256-8 s DE-604 Algebraische Geometrie (DE-588)4001161-6 s Le Barz, Patrick 1948- Verfasser (DE-588)110147987 aut Lecture notes in mathematics 1647 (DE-604)BV000676446 1647 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007413700&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dias, Danielle Le Barz, Patrick 1948- Configuration spaces over Hilbert schemes and applications Lecture notes in mathematics Hilbert schemes Intersection theory Algebraische Geometrie (DE-588)4001161-6 gnd Hilbertsches Schema (DE-588)4159868-4 gnd Konfigurationsraum (DE-588)4199256-8 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4159868-4 (DE-588)4199256-8 |
| title | Configuration spaces over Hilbert schemes and applications |
| title_auth | Configuration spaces over Hilbert schemes and applications |
| title_exact_search | Configuration spaces over Hilbert schemes and applications |
| title_full | Configuration spaces over Hilbert schemes and applications Danielle Dias ; Patrick LeBarz |
| title_fullStr | Configuration spaces over Hilbert schemes and applications Danielle Dias ; Patrick LeBarz |
| title_full_unstemmed | Configuration spaces over Hilbert schemes and applications Danielle Dias ; Patrick LeBarz |
| title_short | Configuration spaces over Hilbert schemes and applications |
| title_sort | configuration spaces over hilbert schemes and applications |
| topic | Hilbert schemes Intersection theory Algebraische Geometrie (DE-588)4001161-6 gnd Hilbertsches Schema (DE-588)4159868-4 gnd Konfigurationsraum (DE-588)4199256-8 gnd |
| topic_facet | Hilbert schemes Intersection theory Algebraische Geometrie Hilbertsches Schema Konfigurationsraum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007413700&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT diasdanielle configurationspacesoverhilbertschemesandapplications AT lebarzpatrick configurationspacesoverhilbertschemesandapplications |