Baum-Bott residue of flags of holomorphic distributions. (English) Zbl 1505.32009
Summary: In this work, we extend the residue theory from flag of holomorphic foliations to flag of holomorphic distributions and we provide an effective way to calculate this class in certain cases. As a consequence, we show that if we consider a flag \(\mathcal{F}=(\mathcal{F}_1,\mathcal{F}_2)\) of holomorphic distributions on \(\mathbb{P}^3\), we get a relation between the degrees of the distributions in the flag, the tangency order of distributions, the Euler character characteristic and the degree of the curve \(C\).
MSC:
| 32A27 | Residues for several complex variables |
| 32M25 | Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions |
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