Dynamical systems and systems of equations

# Lelong numbers of positive harmonic currents directed by singular holomorphic foliations

speaker: Viet-Anh Nguyen (Lille University)

abstract: Let F be a holomorphic foliation by curves defined in a neighborhood of 0 in lC n(n ≥ 2) having 0 as a weakly hyperbolic singularity. Let T be a positive harmonic current directed by F which does not give mass to any of the n coordinate invariant hyperplanes {zj = 0} for 1 ≤ j ≤ n. Then we show that the Lelong number of T at 0 vanishes. Moreover, an application of this local result in the global context is given.

Keywords: singular holomorphic foliation, (weakly) hyperbolic singularity, directed positive harmonic current, directed positive ddc -closed currents, Lelong number.

timetable:
Thu 23 Jun, 14:00 - 15:00, Aula Dini
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