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We study pencils of plane curves $f_{t} = f - t l^{N}$ , t ∈ ℂ, using the notion of polar invariant of the plane curve f = 0 with respect to a smooth curve l = 0. More precisely we compute the jacobian Newton polygon of the generic fiber $f_{t}$ , t ∈ ℂ. The main result gives the description of pencils which have an irreducible fiber. Furthermore we prove some applications of the local properties of pencils to singularities at infinity of polynomials in two complex variables.

Pinceaux linéaires de feuilletages sur CP(3) et conjecture de Brunella.

Dominique Cerveau (2002)

Publicacions Matemàtiques

The general element of a pencil of Cod 1 foliation in CP(3) either has an invariant surface or contains a subfoliation by algebraic curves.

Plane curves with hyperbolic and $C$ -hyperbolic complements

G. Dethloff, M. Zaidenberg (1996)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Plane elliptic systems and monogenic functions in symmetric domains

Sommen, F. (1984)

Proceedings of the 12th Winter School on Abstract Analysis

Pluri-canonical divisors on Kähler manifolds.

M. Levine (1983)

Inventiones mathematicae

Pluricanonical embeddings

Jim Morrow, Hugo Rossi (1981)

Compositio Mathematica

Pluriclosed flow on manifolds with globally generated bundles

Jeffrey Streets (2016)

Complex Manifolds

We show global existence and convergence results for the pluriclosed flow on manifolds for which certain naturally associated tensor bundles are globally generated.

Plurifine potential theory

Jan Wiegerinck (2012)

Annales Polonici Mathematici

We give an overview of the recent developments in plurifine pluripotential theory, i.e. the theory of plurifinely plurisubharmonic functions.

Pluriharmonic extension in proper image domains

Rafał Czyż (2009)

Annales Polonici Mathematici

Let $D_{j}$ be a bounded hyperconvex domain in $ℂ^{n_{j}}$ and set $D = D ₁ \times \dots \times D_{s}$ , j=1,...,s, s ≥ 3. Also let $Ω_{π}$ be the image of D under the proper holomorphic map π. We characterize those continuous functions $f : \partial Ω_{π} \to ℝ$ that can be extended to a real-valued pluriharmonic function in $Ω_{π}$ .

Pluriharmonic functions on symmetric tube domains with BMO boundary values

Ewa Damek, Jacek Dziubański, Andrzej Hulanicki, Jose L. Torrea (2002)

Colloquium Mathematicae

Let 𝓓 be a symmetric Siegel domain of tube type and S be a solvable Lie group acting simply transitively on 𝓓. Assume that L is a real S-invariant second order operator that satisfies Hörmander's condition and annihilates holomorphic functions. Let H be the Laplace-Beltrami operator for the product of upper half planes imbedded in 𝓓. We prove that if F is an L-Poisson integral of a BMO function and HF = 0 then F is pluriharmonic. Some other related results are also considered.

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Phénomène de Hartogs-Bochner dans les variétés CR

Phénomène de Hartogs-Bochner relatif dans une hypersurface réelle 2-concave d'une variété analytique complexe.

Picard-Borel-Eigenschaft und Anwendungen.

Picard-Borel-Räume.

Picard-Zahlen komplexer Tori.

Pick interpolation for a uniform algebra

Pinceaux de courbes planes et invariants polaires