Extension groups of tautological sheaves on Hilbert schemes of points on surfaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Logos-Verl.
2012
|
| Schriftenreihe: | Augsburger Schriften zur Mathematik, Physik und Informatik
20 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | 127 S. |
| ISBN: | 9783832532543 |
Internformat
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| 490 | 1 | |a Augsburger Schriften zur Mathematik, Physik und Informatik |v 20 | |
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Datensatz im Suchindex
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|---|---|
| adam_text |
IMAGE 1
C O N T E N T S
0.1 INTRODUCTION 1
1 P R E L I M I N A R I E S 1 0
1.1 GENERAL NOTATIONS AND CONVENTIONS 10
1.2 COMBINATORICAL NOTATIONS AND PRELIMINARIES 12
1.2.1 SYMMETRIC GROUPS 12
1.2.2 SIGNS 12
1.2.3 MULTI-INDICES 13
1.2.4 PARTIAL DIAGONALS 14
1.2.5 BINOMIAL COEFFICIENTS 14
1.3 GRADED VECTOR SPACES AND THEIR EULER CHARACTERISTICS 15
1.3.1 GRADED VECTOR SPACES 15
1.3.2 GROTHENDIECK GROUPS AND THE EULER CHARACTERISTIC 17
1.4 EQUIVARIANT SHEAVES 18
1.4.1 BASIC DEFINITIONS 18
1.4.2 INFLATION AND RESTRICTION 19
1.4.3 SCHEMES WITH TRIVIAL G-ACTION 20
1.4.4 EQUIVARIANT GEOMETRIC FUNCTORS 20
1.4.5 DERIVED EQUIVARIANT CATEGORIES 22
1.4.6 INJECTIVE AND LOCALLY FREE SHEAVES 22
1.4.7 DERIVED EQUIVARIANT FUNCTORS 23
1.4.8 REPRESENTATIONS AS G-SHEAVES 25
1.4.9 EQUIVARIANT GROTHENDIECK DUALITY 25
1.5 PRELIMINARY LEMMAS 20
1.5.1 DERIVED BIFUNCTORS 26
1.5.2 DANILA'S LEMMA AND COROLLARIES 27
1.5.3 PULL-BACK ALONG REGULAR EMBEDDINGS 29
1.5.4 PARTIAL DIAGONALS AND THE STANDARD REPRESENTATION 33
1.5.5 NORMAL VARIETIES 38
7
HTTP://D-NB.INFO/1028160755
IMAGE 2
2 I M A G E O F T A U T O L O G I C A L S H E A V E S U N D E R T H E B
R I D G E L A N D - K I N G - R E I D E Q U I V A L E N C E 4 0
2.1 THE BRIDGELAND-KING-REID EQUIVALENCE 40
2.2 THE HILBERT SCHEME OF POINTS ON A SURFACE 41
2.3 TAUTOLOGICAL SHEAVES 43
2.4 THE COMPLEX C* 44
2.5 POLYGRAPHS AND THE IMAGE OF TAUTOLOGICAL SHEAVES UNDER I 45
2.6 DESCRIPTION FOR K 2 48
2.7 MULTITOR SPECTRAL SEQUENCE 49
3 C O H O M O L O G I C A L I N V A R I A N T S O F T W I S T E D P R O
D U C T S O F T A U T O L O G I C A L S H E A V E S 5 2
3.1 DESCRIPTION OF PQ*(E^ 52
3.1.1 CONSTRUCTION OF THE 7) AND (PI 52
3.1.2 THE OPEN SUBSET A* + 55
3.1.3 DESCRIPTION OF P*Q*(E^ * * * 56
3.1.4 DESCRIPTION OF (!?["' -?["') 58
3.2 INVARIANTS OF K Q AND THE T \ 59
3.2.1 ORBITS AND THEIR ISOTROPY GROUPS ON THE SETS OF INDICES 59
3.2.2 THE SHEAVES OF INVARIANTS AND THEIR COHOMOLOGY 61
3.3 THE MAP PI ON COHOMOLOGY AND THE CUP PRODUCT 63
3.4 COHOMOLOGY IN THE HIGHEST AND LOWEST DEGREE 65
3.4.1 GLOBAL SECTIONS FOR N K AND X PROJECTIVE 65
3.4.2 COHOMOLOGY IN DEGREE 2N 67
3.5 WEDGE PRODUCTS IN THE CASE OF LINE BUNDLES 67
3.6 TENSOR PRODUCTS OF TAUTOLOGICAL BUNDLES ON A'' 2' AND 69
3.6.1 LONG EXACT SEQUENCES ON X 2 69
3.6.2 THE INVARIANTS ON S 2 X 77
3.6.3 COHOMOLOGY ON X ^ 78
3.6.4 LONG EXACT SEQUENCES ON A'!"' 80
3.7 TENSOR PRODUCTS OF TAUTOLOGICAL BUNDLES ON A ^ 83
3.7.1 RESTRICTION OF LOCAL SECTIONS TO CLOSED SUBVARIETIES 83
3.7.2 DOUBLE TENSOR PRODUCTS 85
3.7.3 TRIPLE TENSOR PRODUCTS 86
3.8 GENERALISATIONS 94
3.8.1 DETERMINANT LINE BUNDLES 94
3.8.2 DERIVED FUNCTORS 95
3.8.3 GENERALISED RESULTS 96
8
IMAGE 3
4 E X T E N S I O N G R O U P S O F T W I S T E D T A U T O L O G I C A
L O B J E C T S 1 0 0
4.1 THE CASE OF TAUTOLOGICAL BUNDLES 101
4.1.1 COMPUTATION OF THE HORNS 101
4.1.2 VANISHING OF THE HIGHER E X T ' ^ - F L 1 1 ' ) , O X " ) 102
4.1.3 VANISHING OF THE HIGHER E2CT'( I'(SL"L), E ( F L " L ) ) 103
4.2 GENERALISATIONS 108
4.2.1 DETERMINANT, LINE BUNDLES 108
4.2.2 PROM TAUTOLOGICAL BUNDLES TO TAUTOLOGICAL OBJECTS 109
4.3 GLOBAL EXT-GROUPS 110
4.4 SPHERICAL AND P"-OBJECTS 112
4.5 PRODUCTS AND INTERPRETATION OF THE RESULTS 114
4.5.1 YONEDA PRODUCTS, THE KUNNETH ISOMORPHISM AND SIGNS 114
4.5.2 YONEDA PRODUCTS FOR TWISTED TAUTOLOGICAL OBJECTS 115
4.5.3 INTERPRETATION OF THE FORMULAS 119
4.5.4 THE TRACE MAP AND THE CUP PRODUCT 122
R E F E R E N C E S 1 2 4
9 |
| any_adam_object | 1 |
| author | Krug, Andreas 1983- |
| author_GND | (DE-588)1029726515 |
| author_facet | Krug, Andreas 1983- |
| author_role | aut |
| author_sort | Krug, Andreas 1983- |
| author_variant | a k ak |
| building | Verbundindex |
| bvnumber | BV041128537 |
| classification_rvk | SK 240 |
| ctrlnum | (OCoLC)830879347 (DE-599)DNB1028160755 |
| dewey-full | 516.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| institution | BVB |
| isbn | 9783832532543 |
| language | English |
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| physical | 127 S. |
| publishDate | 2012 |
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| series | Augsburger Schriften zur Mathematik, Physik und Informatik |
| series2 | Augsburger Schriften zur Mathematik, Physik und Informatik |
| spelling | Krug, Andreas 1983- Verfasser (DE-588)1029726515 aut Extension groups of tautological sheaves on Hilbert schemes of points on surfaces Andreas Krug Berlin Logos-Verl. 2012 127 S. txt rdacontent n rdamedia nc rdacarrier Augsburger Schriften zur Mathematik, Physik und Informatik 20 Augsburg, Univ., Diss., 2012 Äquivariante Garbe (DE-588)4787022-9 gnd rswk-swf Hilbertsches Schema (DE-588)4159868-4 gnd rswk-swf Erweiterungsgruppe (DE-588)4721329-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Hilbertsches Schema (DE-588)4159868-4 s Äquivariante Garbe (DE-588)4787022-9 s Erweiterungsgruppe (DE-588)4721329-2 s DE-604 Augsburger Schriften zur Mathematik, Physik und Informatik 20 (DE-604)BV017601953 20 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4185638&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026104409&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krug, Andreas 1983- Extension groups of tautological sheaves on Hilbert schemes of points on surfaces Augsburger Schriften zur Mathematik, Physik und Informatik Äquivariante Garbe (DE-588)4787022-9 gnd Hilbertsches Schema (DE-588)4159868-4 gnd Erweiterungsgruppe (DE-588)4721329-2 gnd |
| subject_GND | (DE-588)4787022-9 (DE-588)4159868-4 (DE-588)4721329-2 (DE-588)4113937-9 |
| title | Extension groups of tautological sheaves on Hilbert schemes of points on surfaces |
| title_auth | Extension groups of tautological sheaves on Hilbert schemes of points on surfaces |
| title_exact_search | Extension groups of tautological sheaves on Hilbert schemes of points on surfaces |
| title_full | Extension groups of tautological sheaves on Hilbert schemes of points on surfaces Andreas Krug |
| title_fullStr | Extension groups of tautological sheaves on Hilbert schemes of points on surfaces Andreas Krug |
| title_full_unstemmed | Extension groups of tautological sheaves on Hilbert schemes of points on surfaces Andreas Krug |
| title_short | Extension groups of tautological sheaves on Hilbert schemes of points on surfaces |
| title_sort | extension groups of tautological sheaves on hilbert schemes of points on surfaces |
| topic | Äquivariante Garbe (DE-588)4787022-9 gnd Hilbertsches Schema (DE-588)4159868-4 gnd Erweiterungsgruppe (DE-588)4721329-2 gnd |
| topic_facet | Äquivariante Garbe Hilbertsches Schema Erweiterungsgruppe Hochschulschrift |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4185638&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026104409&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV017601953 |
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