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Flatness testing over singular bases

Janusz Adamus, Hadi Seyedinejad (2013)

Annales Polonici Mathematici

We show that non-flatness of a morphism φ:X→ Y of complex-analytic spaces with a locally irreducible target of dimension n manifests in the existence of vertical components in the n-fold fibred power of the pull-back of φ to the desingularization of Y. An algebraic analogue follows: Let R be a locally (analytically) irreducible finite type ℂ-algebra and an integral domain of Krull dimension n, and let S be a regular n-dimensional algebra of finite type over R (but not necessarily a finite R-module),...

Foliations by curves with curves as singularities

M. Corrêa Jr, A. Fernández-Pérez, G. Nonato Costa, R. Vidal Martins (2014)

Annales de l’institut Fourier

Let ℱ be a holomorphic one-dimensional foliation on ℙ n such that the components of its singular locus Σ are curves C i and points p j . We determine the number of p j , counted with multiplicities, in terms of invariants of ℱ and C i , assuming that ℱ is special along the C i . Allowing just one nonzero dimensional component on Σ , we also prove results on when the foliation happens to be determined by its singular locus.

Foliations in algebraic surfaces having a rational first integral.

Alexis García Zamora (1997)

Publicacions Matemàtiques

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.

Foliations on the complex projective plane with many parabolic leaves

Marco Brunella (1994)

Annales de l'institut Fourier

We prove that a foliation on C P 2 with hyperbolic singularities and with “many" parabolic leaves (i.e. leaves without Green functions) is in fact a linear foliation. This is done in two steps: first we prove that there exists an algebraic leaf, using the technique of harmonic measures, then we show that the holonomy of this leaf is linearizable, from which the result follows easily.

Foliations with complex leaves

Giuliana Gigante, Giuseppe Tomassini (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let X be a smooth foliation with complex leaves and let D be the sheaf of germs of smooth functions, holomorphic along the leaves. We study the ringed space X , D . In particular we concentrate on the following two themes: function theory for the algebra D ⁢ X and cohomology with values in D .

Foliazioni di Monge-Ampère e classificazione olomorfa

Giorgio Patrizio (2005)

Bollettino dell'Unione Matematica Italiana

Si illustrano alcuni sviluppi della teoria delle foliazioni di Monge-Ampère e delle sue applicazioni alla classificazione delle varietà complesse non compatte.

Front d'onde et propagation des singularités pour un vecteur-distribution

Dominique Manchon (1999)

Colloquium Mathematicae

We define the wave front set of a distribution vector of a unitary representation in terms of pseudo-differential-like operators [M2] for any real Lie group G. This refines the notion of wave front set of a representation introduced by R. Howe [Hw]. We give as an application a necessary condition so that a distribution vector remains a distribution vector for the restriction of the representation to a closed subgroup H, and we give a propagation of singularities theorem for distribution vectors.

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