منابع مشابه
Foliations in Algebraic Surfaces Having a Rational First Integral
Given a foliation F in an algebraic surface having a rational first integral a genus formula for the general solution is obtained. In the case S = P2 some new counter-examples to the classic formulation of the Poincaré problem are presented. If S is a rational surface and F has singularities of type (1, 1) or (1,−1) we prove that the general solution is a non-singular curve.
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The main objective of this article is to study the topology of the fibers of a generic rational function of the type F p Gq in the projective space of dimension two. We will prove that the action of the monodromy group on a single Lefschetz vanishing cycle δ generates the first homology group of a generic fiber of F p Gq . In particular, we will prove that for any two Lefschetz vanishing cycles...
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We show that the singular holomorphic foliations induced by dominant quasi-homogeneous rational maps fill out irreducible components of the space Fq(r, d) of singular foliations of codimension q and degree d on the complex projective space P , when 1 ≤ q ≤ r − 2. We study the geometry of these irreducible components. In particular we prove that they are all rational varieties and we compute the...
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In this paper, the technique of foliations in characteristic p is used to investigate the difference between rational connectedness and separable rational connectedness in positive characteristic. The notion of being freely rationally connected is defined; a variety is freely rationally connected if a general pair of points can be connected by a free rational curve. It is proved that a freely r...
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The integral of a rational function proposed as a question in Mathematics Stack Exchange is evaluated. The integrand has a polynomial of degree 4 as denominator. A natural extension to degree 8 is shown to vanish.
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ژورنال
عنوان ژورنال: Proyecciones (Antofagasta)
سال: 2005
ISSN: 0716-0917
DOI: 10.4067/s0716-09172005000200006