Geometry of universal embedding spaces for almost complex
manifolds

J 2024

Geometry of universal embedding spaces for almost complex manifolds

CLEMENTE, Gabriella Alexandrea

Basic information

Original name

Geometry of universal embedding spaces for almost complex manifolds

Authors

CLEMENTE, Gabriella Alexandrea

Edition

Archivum Mathematicum, Brno, Masaryk University, 2024, 0044-8753

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Czech Republic

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.5817/AM2024-1-35

UT WoS

001167636800002

Keywords in English

almost-complex manifolds; complex structures; fiber bundles; integrability; Nijenhuis tensor; obstruction theory; transverse embeddings; vector bundles

Abstract

V originále

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.

Links

MUNI/A/1099/2022, interní kód MU

Name: Specifický výzkum v odborné a učitelské matematice 2023

Investor: Masaryk University

Citovat

CLEMENTE, Gabriella Alexandrea. Geometry of universal embedding spaces for almost complex manifolds. 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.

@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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