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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2012, Issue 667


Semicomplete meromorphic vector fields on complex surfaces

Adolfo Guillot
  • Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autónoma de México, A.P. 273-3 Admon. 3, Cuernavaca, Morelos, 62251, Mexico
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/ Julio Rebelo
Published Online: 2011-08-12 | DOI: https://doi.org/10.1515/CRELLE.2011.127


We study semicomplete meromorphic vector fields on complex surfaces, that is, vector fields whose solutions are single-valued in restriction to the open set where the vector field is holomorphic. We show that, up to a birational transformation, a compact connected component of the curve of poles is either a rational or an elliptic curve of null self-intersection or it has the combinatorics of a singular fiber of an elliptic fibration. This result is then globalized by proving that, always up to a birational transformation, a semicomplete meromorphic vector field on a compact complex Kähler surface must satisfy at least one of the following conditions: to be globally holomorphic, to possess a non-trivial meromorphic first integral or to preserve a fibration. In particular, this extends the results established by Brunella for complete polynomial vector fields in the complex plane to the context of semicomplete ones.

About the article

Received: 2009-04-01

Revised: 2010-07-09

Published Online: 2011-08-12

Published in Print: 2012-06-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2012, Issue 667, Pages 27–65, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2011.127.

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