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arXiv · 1212.5793

Existence of the directional tangent cone to a positive current

Haithem Hawari·Jawhar Hbil·Noureddine Ghiloufi
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Abstract

In this paper, we start by proving the existence of the strict transform of a positive current $T$ as soon as its $j^{th}$ currents, $T_j$, are plurisubharmonics or plurisuperharmonics. Then, with a suitable condition on $T_j$, we show the existence of the directional tangent cone to $T$. In the particular case, when $T$ is closed, we give a second condition independent to the previous one.

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Haithem Hawari, Jawhar Hbil, Noureddine Ghiloufi. 2012-12-23. Existence of the directional tangent cone to a positive current. https://arxiv.org/abs/1212.5793

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