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Frobenius theorem for foliations on singular varieties
No full textInternational audienceWe generalize Frobenius singular theorem due to Malgrange, for a large class of codimension one holomorphic foliations on singular analytic subsets of C-N
A structural theorem for codimension-one foliations on , with an application to degree-three foliations
No full textInternational audienceLet be a codimension-one foliation on : for each point we define as the order of the first non-zero jet of a holomorphic 1-form defining at . The singular set of is . We prove (main Theorem 1.2) that a foliation satisfying for all has a non-constant rational first integral. Using this fact we are able to prove that any foliation of degree-three on , with , is either the pull-back of a foliation on , or has a transverse affine structure with poles. This extends previous results for foliations of degree at most two
A structural theorem for codimension-one foliations on \protect \mathbb{P}^n, , with an application to degree-three foliations
No full textHypersurfaces exceptionnelles des endomorphismes de CP(n)
No full textInternational audienceOn étudie les hypersurfaces exceptionnelles pour les applications holomorphes de CopfPopf(n). On montre qu'une telle hypersurface n'est jamais lisse dès que son degré est plus grand que deux. Exceptional hypersurfaces for holomorphic endomorphisms of CopfPopf(n) are studied. We prove that such an hypersurface is not smooth as soon as its degree is greater than two
Codimension two holomorphic foliations
No full textInternational audienceThis paper is devoted to the study of codimension two holomorphic foliations and distributions. We prove the stability of complete intersection of codimension two distributions and foliations in the local case. Converserly we show the existence of codimension two foliations which are not contained in any codimension one foliation. We study problems related to the singular locus and we classify homogeneous foliations of small degree
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