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Equivalence of Neighborhoods of Embedded Compact Complex Manifolds and Higher Codimension Foliations
We consider an embedded n-dimensional compact complex manifold in n+d dimensional complex manifolds. We are interested in the holomorphic classification of neighborhoods as part of Grauert’s formal principle program. We will give conditions ensuring that a neighborhood of C in M is biholomorphic to a neighborhood of the zero section of its normal bundle. This extends Arnold’s result about neighborhoods of a complex torus in a surface. We also prove the existence of a holomorphic foliation in Mn+d having C as a compact leaf, extending Ueda’s theory to the high codimension case. Both problems appear as a kind of linearization problems involving small divisors conditions arising from solutions to their cohomological equations.
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- Award ID(s):
- 2054989
- PAR ID:
- 10320369
- Date Published:
- Journal Name:
- Arnold mathematical journal
- Volume:
- 8
- ISSN:
- 2199-6792
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s40598-021-00192-w
