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arXiv · 1410.3527

2-dimensional Lie algebras and separatrices for vector fields on (C^3,0)

Julio C. Rebelo·Helena Reis
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Abstract

We show that holomorphic vector fields on (C^3,0) have separatrices provided that they are embedded in a rank 2 representation of a two-dimensional Lie algebra. In turn, this result enables us to show that the second jet of a holomorphic vector field defined on a compact complex manifold M of dimension 3 cannot vanish at an isolated singular point provided that M carries more than a single holomorphic vector field.

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Julio C. Rebelo, Helena Reis. 2014-10-13. 2-dimensional Lie algebras and separatrices for vector fields on (C^3,0). https://arxiv.org/abs/1410.3527

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