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Unipotent reduction and the Poincare Problem

A. G. Zamora
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Abstract

The Poincare Problem can be reduced to a problem on fibered surfaces, concretely, to bound the genus of the fibration by means of numerical information of the canonical sheaf of the associated foliation. In this paper we: 1. explain how this reduction can be carried out, 2. apply unipotent reduction to obtain some possible answers to the problem, 3. obtain an answer under some hypotheses on the eigenvalues of the singularities of the foliation

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A. G. Zamora. 2005-06-09. Unipotent reduction and the Poincare Problem. https://arxiv.org/abs/math/0301258

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