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@article{2368923,
author = {Clemente, Gabriella Alexandrea},
article_location = {Brno},
article_number = {1},
doi = {http://dx.doi.org/10.5817/AM2024-1-35},
keywords = {almost-complex manifolds; complex structures; fiber bundles; integrability; Nijenhuis tensor; obstruction theory; transverse embeddings; vector bundles},
language = {eng},
issn = {0044-8753},
journal = {Archivum Mathematicum},
title = {Geometry of universal embedding spaces for almost complex manifolds},
url = {https://dml.cz/handle/10338.dmlcz/152026},
volume = {60},
year = {2024}
}
TY - JOUR
ID - 2368923
AU - Clemente, Gabriella Alexandrea
PY - 2024
TI - Geometry of universal embedding spaces for almost complex manifolds
JF - Archivum Mathematicum
VL - 60
IS - 1
SP - 35-60
EP - 35-60
PB - Masaryk University
SN - 00448753
KW - almost-complex manifolds
KW - complex structures
KW - fiber bundles
KW - integrability
KW - Nijenhuis tensor
KW - obstruction theory
KW - transverse embeddings
KW - vector bundles
UR - https://dml.cz/handle/10338.dmlcz/152026
N2 - 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.
ER -
CLEMENTE, Gabriella Alexandrea. Geometry of universal embedding spaces for almost complex manifolds. \textit{Archivum Mathematicum}. Brno: Masaryk University, 2024, vol.~60, No~1, p.~35-60. ISSN~0044-8753. Available from: https://dx.doi.org/10.5817/AM2024-1-35.
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