Lelong–Poincaré formula in symplectic and almost complex geometry

In this paper, we present two applications of the theory of singular connections developed by Harvey and Lawson (1993). The first one is a version of the Lelong–Poincaré formula with estimates for sections of vector bundles over an almost complex manifold. The second one is a convergence theorem for...

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Bibliographic Details
Published in:Expositiones mathematicae 2020-09, Vol.38 (3), p.337-364
Main Authors: Mazzilli, Emmanuel, Sukhov, Alexandre
Format: Article
Language:English
Subjects:
Almost complex manifold
Complex vector bundle
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Divisor
Mathematics
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Summary:In this paper, we present two applications of the theory of singular connections developed by Harvey and Lawson (1993). The first one is a version of the Lelong–Poincaré formula with estimates for sections of vector bundles over an almost complex manifold. The second one is a convergence theorem for divisors associated to a general family of symplectic submanifolds constructed by Donaldson (1996) (the case of hypersurfaces) and by Auroux in (1997) (for arbitrary dimensional submanifolds).
ISSN:0723-0869
1878-0792
DOI:10.1016/j.exmath.2019.04.004