INTEGRABILITY OF VECTOR FIELDS AND MEROMORPHIC SOLUTIONS

• Type: Article in International Scientific Journal
• Date: 2023

Authors

Julio Rebelo (Author) Other; Helena Reis (Author) FEP

Journal

Title: Moscow Mathematical Journal

Vol. 23 No. 4

Pages: 591-624

ISSN: 1609-3321

Publisher: Independent University of Moscow

Indexing

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Other information

Authenticus ID: P-00Z-FG7

DOI: 10.17323/1609-4514-2023-23-4-591-624

Abstract (EN): Let F be a one-dimensional holomorphic foliation defined on a complex projective manifold and consider a meromorphic vector field X tangent to F. In this paper, we prove that if the set of integral curves of X that are given by meromorphic maps defined on C is large enough, then the restriction of F to any invariant complex 2-dimensional analytic set admits a first integral of Liouvillean type. In particular, on C-3, every rational vector field whose solutions are meromorphic functions defined on C admits an invariant analytic set of dimension 2 such that the restriction of the vector field to it yields a Liouville integrable foliation.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 34