On the algebraic hypersurfaces invariant by weighted projective foliations

2009/01/13 by Correa, Mauricio
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.0901.1710

Abstract

In this work we study some problems related with algebraic hypersurfaces invariant by foliations on weighted projective spaces ℙ_ℂ(\varpi₀,...,\varpi_n) generalizing some results known for \p, as for example: the number of singularities, with multiplicities, contained in the invariant quasi-smooth hypersurfaces; Poincare problem on weighted projective plane and the number of the hypersurfaces, of a degree fixed, invariant by a foliation on ℙ_ℂ(\varpi₀,...,\varpi_n) which does not admit a rational first integral.

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