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Residues of singular holomorphic distributions. (English) Zbl 1317.32065

Blanlœil, Vincent (ed.) et al., Singularities in geometry and topology, Strasbourg 2009. Proceedings of the 5th Franco-Japanese symposium on singularities, Strasbourg, France, August 24–28, 2009. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-118-7/pbk). IRMA Lectures in Mathematics and Theoretical Physics 20, 207-247 (2012).
Summary: We present two types of residue theories for singular holomorphic distributions. The first one is for certain Chern polynomials of the normal sheaf of a distribution and the residues arise from the vanishing, by rank reason, of the relevant characteristic classes on the non-singular part. The second one is for certain Atiyah polynomials of vector bundles admitting an action of a distribution and the residues arise from the Bott type vanishing theorem on the non-singular part.
For the entire collection see [Zbl 1255.14001].

MSC:

32S65 Singularities of holomorphic vector fields and foliations
58A30 Vector distributions (subbundles of the tangent bundles)
32A27 Residues for several complex variables
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