Semi-complete vector fields of saddle-node type in ℂⁿ

Reis, Helena

doi:10.1090/S0002-9947-08-04516-9

Semi-complete vector fields of saddle-node type in $\mathbb {C}^n$
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Trans. Amer. Math. Soc. 360 (2008), 6611-6630 Request permission

Abstract:

We classify the foliations associated to codimension $1$ saddle-node vector fields on $\mathbb {C}^n$, with an isolated singularity, admitting a semi-complete representative. This will be done under some further assumptions that are generic in dimension $3$. These singularities play an essential role in the program to classify semi-complete vector fields in dimension $3$.

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