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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