A Dolbeault lemma for temperate currents

Henri Skoda

Corpus ID: 214641228

A Dolbeault lemma for temperate currents

@article{Skoda2020ADL,
  title={A Dolbeault lemma for temperate currents},
  author={Henri Skoda},
  journal={arXiv: Complex Variables},
  year={2020}
}

Henri Skoda

Published 2020

Mathematics

arXiv: Complex Variables

We consider a bounded open Stein subset $\Omega$ of a complex Stein manifold $X$ of dimension $n$. We prove that if $f$ is a current on $X$ of bidegree $(p,q+1)$, $\bar\partial$-closed on $\Omega$, we can find a current $u$ on $X$ of bidegree $(p,q)$ which is a solution of the equation $\bar\partial u=f$ in $\Omega$. In other words, we prove that the Dolbeault complex of temperate currents on $\Omega$ (i.e. currents on $\Omega$ which extend to currents on $X$) is concentrated in degree $0… CONTINUE READING

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