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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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