Cyclic coverings, Calabi-Yau manifolds and complex multiplication:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Hochschulschrift/Dissertation Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2009
|
| Schriftenreihe: | Lecture notes in mathematics
1975 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017389913&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | IX, 228 S. graph. Darst. |
| ISBN: | 9783642006388 9783642006395 |
Internformat
MARC
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|---|---|---|---|
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| 100 | 1 | |a Rohde, Jan Christian |d 1978- |e Verfasser |0 (DE-588)138183627 |4 aut | |
| 245 | 1 | 0 | |a Cyclic coverings, Calabi-Yau manifolds and complex multiplication |c Jan Christian Rohde |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a IX, 228 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1975 | |
| 502 | |a Zugl.: Duisburg-Essen, Univ., Diss., 2007 | ||
| 650 | 4 | |a Calabi-Yau manifolds | |
| 650 | 4 | |a Multiplication, Complex | |
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| 650 | 0 | 7 | |a Überdeckung |g Mathematik |0 (DE-588)4186551-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Shimura-Mannigfaltigkeit |0 (DE-588)4181143-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Hodge-Struktur |0 (DE-588)4406134-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Komplexe Multiplikation |0 (DE-588)4164903-5 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
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| 689 | 0 | 2 | |a Shimura-Mannigfaltigkeit |0 (DE-588)4181143-4 |D s |
| 689 | 0 | 3 | |a Komplexe Multiplikation |0 (DE-588)4164903-5 |D s |
| 689 | 0 | |5 DE-604 | |
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| 830 | 0 | |a Lecture notes in mathematics |v 1975 |w (DE-604)BV000676446 |9 1975 | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 001z 2001 B 999-1975 |
|---|---|
| DE-BY-TUM_katkey | 1693623 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010151498 |
| _version_ | 1821933674776494081 |
| adam_text | Contents
Introduction
................................................................ 1
1 An
introduction
to Hodge structures and Shimura
varieties
.................................................................. 11
1.1
The basic definitions
................................................ 12
1.2
Jacobians, Polarizations and Riemann s Theorem
................ 19
1.3
The definition of the Shimura datum
.............................. 25
1.4
Hermitian symmetric domains
..................................... 35
1.5
The construction of Shimura varieties
............................. 43
1.6
The definition of complex multiplication
.......................... 45
1.7
Criteria and conjectures for complex multiplication
.............. 50
2
Cyclic covers of the
projective
line
............................... 59
2.1
Description of a cyclic cover of the
projective
line
............... 60
2.2
The local system corresponding to a cyclic cover
................. 62
2.3
The cohomology of a cover
......................................... 66
2.4
Cyclic covers with complex multiplication
........................ 67
3
Some preliminaries for families of cyclic covers
................ 71
3.1
The generic Hodge group
........................................... 71
3.2
Families of covers of the
projective
line
........................... 73
3.3
The homology and the monodromy representation
............... 76
4
The Galois group decomposition of the Hodge structure
___ 79
4.1
The Galois group representation on the first cohomology
....... 79
4.2
Quotients of covers and Hodge group decomposition
............ 84
4.3
Upper bounds for the Mumford-Tate groups
of the direct summands
............................................. 85
4.4
A criterion for complex multiplication
............................ 88
viii Contents
5
The computation of the Hodge group
............................ 91
5.1
The monodromy group of an eigenspace
.......................... 92
5.2
The Hodge group of a general direct summand
................... 99
5.3
A criterion for the reaching of the upper bound
..................102
5.4
The exceptional cases
...............................................
Ю6
5.5
The Hodge group of a universal family
of hyperelliptic curves
..............................................
HO
5.6
The complete generic Hodge group
................................115
6
Examples of families with dense sets of complex
multiplication fibers
..................................................121
6.1
The necessary condition
SINT
....................................121
6.2
The application of
SINT
for the more complicated cases
.......129
6.3
The complete lists of examples
.....................................136
6.4
The derived variations of Hodge structures
.......................137
7
The construction of Calabi-Yau manifolds
with complex multiplication
........................................ 143
7.1
The basic construction and complex multiplication
..............143
7.2
The Borcea-
Voisin
tower
............................................147
7.3
The Viehweg-Zuo tower
............................................150
7.4
A new example
......................................................153
8
The degree
3
case
.....................................................157
8.1
Prelude
...............................................................158
8.2
A modified version of the method of Viehweg and Zuo
..........162
8.3
The resulting family and its involutions
...........................166
9
Other examples and variations
.....................................169
9.1
The degree
3
case
...................................................170
9.2
Calabi-Yau 3-manifolds obtained by quotients
of degree
3...........................................................172
9.3
The degree
4
case
...................................................178
9.4
Involutions on the quotients of the degree
4
example
............180
9.5
The extended automorphism group of the degree
4
example
___183
9.6
The automorphism group of the degree
5
example
by Viehweg and Zuo
................................................185
10
Examples of CMCY families of 3-manifolds
and their invariants
................................................... 187
10.1
The length of the Yukawa coupling
................................187
10.2
Examples obtained by degree
2
quotients
.........................188
10.3
Examples obtained by degree
3
quotients
.........................189
10.4
Outlook onto quotients by cyclic groups of high order
...........196
Contents
ix
11
Maximal families of CMCY type
.................................199
11.1
Facts about involutions and quotients of .O-surfaces
............199
11.2
The associated Shimura datum
....................................201
11.3
The examples
........................................................203
A Examples of Calabi-Yau 3-manifolds with complex
multiplication
..........................................................209
A.I Construction by degree
2
coverings of a ruled surface
...........209
A.2 Construction by degree
2
coverings of P2
.........................214
A.3 Construction by a degree
3
quotient
...............................217
References
...................................................................223
Index
.........................................................................227
|
| any_adam_object | 1 |
| author | Rohde, Jan Christian 1978- |
| author_GND | (DE-588)138183627 |
| author_facet | Rohde, Jan Christian 1978- |
| author_role | aut |
| author_sort | Rohde, Jan Christian 1978- |
| author_variant | j c r jc jcr |
| building | Verbundindex |
| bvnumber | BV035470235 |
| callnumber-first | Q - Science |
| callnumber-label | QA3 |
| callnumber-raw | QA3 |
| callnumber-search | QA3 |
| callnumber-sort | QA 13 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| classification_tum | MAT 142f MAT 146f MAT 144f |
| ctrlnum | (OCoLC)390521372 (DE-599)BVBBV035470235 |
| dewey-full | 516.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.353 |
| dewey-search | 516.353 |
| dewey-sort | 3516.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV035470235 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:33:14Z |
| institution | BVB |
| isbn | 9783642006388 9783642006395 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017389913 |
| oclc_num | 390521372 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-824 DE-91G DE-BY-TUM DE-384 DE-11 DE-83 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-824 DE-91G DE-BY-TUM DE-384 DE-11 DE-83 DE-188 |
| physical | IX, 228 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spellingShingle | Rohde, Jan Christian 1978- Cyclic coverings, Calabi-Yau manifolds and complex multiplication Lecture notes in mathematics Calabi-Yau manifolds Multiplication, Complex Calabi-Yau-Mannigfaltigkeit (DE-588)4440893-6 gnd Überdeckung Mathematik (DE-588)4186551-0 gnd Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd Hodge-Struktur (DE-588)4406134-1 gnd Komplexe Multiplikation (DE-588)4164903-5 gnd |
| subject_GND | (DE-588)4440893-6 (DE-588)4186551-0 (DE-588)4181143-4 (DE-588)4406134-1 (DE-588)4164903-5 (DE-588)4113937-9 |
| title | Cyclic coverings, Calabi-Yau manifolds and complex multiplication |
| title_auth | Cyclic coverings, Calabi-Yau manifolds and complex multiplication |
| title_exact_search | Cyclic coverings, Calabi-Yau manifolds and complex multiplication |
| title_full | Cyclic coverings, Calabi-Yau manifolds and complex multiplication Jan Christian Rohde |
| title_fullStr | Cyclic coverings, Calabi-Yau manifolds and complex multiplication Jan Christian Rohde |
| title_full_unstemmed | Cyclic coverings, Calabi-Yau manifolds and complex multiplication Jan Christian Rohde |
| title_short | Cyclic coverings, Calabi-Yau manifolds and complex multiplication |
| title_sort | cyclic coverings calabi yau manifolds and complex multiplication |
| topic | Calabi-Yau manifolds Multiplication, Complex Calabi-Yau-Mannigfaltigkeit (DE-588)4440893-6 gnd Überdeckung Mathematik (DE-588)4186551-0 gnd Shimura-Mannigfaltigkeit (DE-588)4181143-4 gnd Hodge-Struktur (DE-588)4406134-1 gnd Komplexe Multiplikation (DE-588)4164903-5 gnd |
| topic_facet | Calabi-Yau manifolds Multiplication, Complex Calabi-Yau-Mannigfaltigkeit Überdeckung Mathematik Shimura-Mannigfaltigkeit Hodge-Struktur Komplexe Multiplikation Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017389913&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT rohdejanchristian cycliccoveringscalabiyaumanifoldsandcomplexmultiplication |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 MAT 001z 2001 B 999-1975 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |