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A Schwarz lemma for correspondences and applications.

Kaushal Verma (2003)

Publicacions Matemàtiques

A version of the Schwarz lemma for correspondences is studied. Two applications are obtained namely, the 'non-increasing' property of the Kobayashi metric under correspondences and a weak version of the Wong-Rosay theorem for convex, finite type domains admitting a 'non-compact' family of proper correspondences.

Concave domains with trivial biholomorphic invariants

Witold Jarnicki, Nikolai Nikolov (2002)

Annales Polonici Mathematici

It is proved that if F is a convex closed set in ℂⁿ, n ≥2, containing at most one (n-1)-dimensional complex hyperplane, then the Kobayashi metric and the Lempert function of ℂⁿ∖ F identically vanish.

Degeneracy of holomorphic maps via orbifolds

Erwan Rousseau (2012)

Bulletin de la Société Mathématique de France

We use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal surfaces and complements of singular plane curves.

Étude des jets de Demailly-Semple en dimension 3

Erwan Rousseau (2006)

Annales de l’institut Fourier

Dans cet article nous faisons l’étude algébrique des jets de Demailly-Semple en dimension 3 en utilisant la théorie des invariants des groupes non réductifs. Cette étude fournit la caractérisation géométrique du fibré des jets d’ordre 3 sur une variété de dimension 3 et permet d’effectuer, par Riemann-Roch, un calcul de caractéristique d’Euler.

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