| Title:
|
Geometry of universal embedding spaces for almost complex manifolds (English) |
| Author:
|
Clemente, Gabriella |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
60 |
| Issue:
|
1 |
| Year:
|
2024 |
| Pages:
|
35-60 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate the geometry of universal embedding spaces for compact almost-complex manifolds of a given dimension, and related constructions that allow for an extrinsic study of the integrability of almost-complex structures. These embedding spaces were introduced by J-P. Demailly and H. Gaussier, and are complex algebraic analogues of twistor spaces. Their goal was to study a conjecture made by F. Bogomolov asserting the “transverse embeddability” of arbitrary compact complex manifolds into foliated algebraic varieties. In this work, we introduce a more general category of universal embedding spaces, and elucidate the geometric structure of related bundles, such as the integrability locus characterizing integrable almost-complex structures. Our approach could potentially lead to finding new obstructions to the existence of a complex structure, which may be useful for tackling Yau’s Challenge. (English) |
| Keyword:
|
almost-complex manifolds |
| Keyword:
|
complex structures |
| Keyword:
|
integrability |
| Keyword:
|
Nijenhuis tensor |
| Keyword:
|
obstruction theory |
| Keyword:
|
transverse embeddings |
| Keyword:
|
fiber bundles |
| Keyword:
|
vector bundles |
| MSC:
|
32L05 |
| MSC:
|
32Q40 |
| MSC:
|
32Q60 |
| idZBL:
|
Zbl 07830505 |
| idMR:
|
MR4709720 |
| DOI:
|
10.5817/AM2024-1-35 |
| . |
| Date available:
|
2024-02-07T14:13:12Z |
| Last updated:
|
2024-08-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152026 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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