Geometry of universal embedding spaces for almost complex manifolds
Archivum Mathematicum (2024)
- Issue: 1, page 35-60
- ISSN: 0044-8753
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topClemente, Gabriella. "Geometry of universal embedding spaces for almost complex manifolds." Archivum Mathematicum (2024): 35-60. <http://eudml.org/doc/299188>.
@article{Clemente2024,
abstract = {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.},
author = {Clemente, Gabriella},
journal = {Archivum Mathematicum},
keywords = {almost-complex manifolds; complex structures; integrability; Nijenhuis tensor; obstruction theory; transverse embeddings; fiber bundles; vector bundles},
language = {eng},
number = {1},
pages = {35-60},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Geometry of universal embedding spaces for almost complex manifolds},
url = {http://eudml.org/doc/299188},
year = {2024},
}
TY - JOUR
AU - Clemente, Gabriella
TI - Geometry of universal embedding spaces for almost complex manifolds
JO - Archivum Mathematicum
PY - 2024
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
IS - 1
SP - 35
EP - 60
AB - 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.
LA - eng
KW - almost-complex manifolds; complex structures; integrability; Nijenhuis tensor; obstruction theory; transverse embeddings; fiber bundles; vector bundles
UR - http://eudml.org/doc/299188
ER -
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