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Intertwined mappings

Jean Ecalle, Bruno Vallet (2004)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Intrinsic pseudo-volume forms for logarithmic pairs

Thomas Dedieu (2010)

Bulletin de la Société Mathématique de France

We study an adaptation to the logarithmic case of the Kobayashi-Eisenman pseudo-volume form, or rather an adaptation of its variant defined by Claire Voisin, for which she replaces holomorphic maps by holomorphic K -correspondences. We define an intrinsic logarithmic pseudo-volume form Φ X , D for every pair ( X , D ) consisting of a complex manifold X and a normal crossing Weil divisor D on X , the positive part of which is reduced. We then prove that Φ X , D is generically non-degenerate when X is projective and K X + D ...

Invariance for multiples of the twisted canonical bundle

Benoît Claudon (2007)

Annales de l’institut Fourier

Let 𝒳 Δ a smooth projective family and ( L , h ) a pseudo-effective line bundle on 𝒳 (i.e. with a non-negative curvature current Θ h L ). In its works on invariance of plurigenera, Y.-T. Siu was interested in extending sections of m K 𝒳 0 + L (defined over the central fiber of the family 𝒳 0 ) to sections of m K 𝒳 + L . In this article we consider the following problem: to extend sections of m ( K 𝒳 + L ) . More precisely, we show the following result: assuming the triviality of the multiplier ideal sheaf ( 𝒳 0 , h | 𝒳 0 ) , any section of m ( K 𝒳 0 + L ) extends to 𝒳  ; in other...

Invariance of domain in o-minimal structures

Rafał Pierzchała (2001)

Annales Polonici Mathematici

The aim of this paper is to prove the theorem on invariance of domain in an arbitrary o-minimal structure. We do not make use of the methods of algebraic topology and the proof is based merely on some basic facts about cells and cell decompositions.

Invariant connections and invariant holomorphic bundles on homogeneous manifolds

Indranil Biswas, Andrei Teleman (2014)

Open Mathematics

Let X be a differentiable manifold endowed with a transitive action α: A×X→X of a Lie group A. Let K be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects: equivalence classes of α-invariant K-connections on X α-invariant gauge classes of K-connections on X, andα-invariant isomorphism classes of pairs (Q,P) consisting of a holomorphic Kℂ-bundle Q → X and a K-reduction P of Q (when...

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