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

• Type: Article in International Scientific Journal
• Date: 2016

Authors

Rebelo, JC (Author) Other; Helena Reis (Author) FEP

Journal

Title: JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES

Vol. 105

Pages: 248-264

ISSN: 0021-7824

Publisher: Palgrave Macmillan

Indexing

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Other information

Authenticus ID: P-00K-069

DOI: 10.1016/j.matpur.2015.10.005

Abstract (EN): 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. As an application of this result we show, in particular, 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 17