$L^2$-theory for the $\bar{\partial}$-operator on complex spaces with isolated singularities

Jean Ruppenthal

$L^2$-theory for the $\bar{\partial}$-operator on complex spaces with isolated singularities

Complex Variables 2015-02-24 v3

Authors: Jean Ruppenthal

Abstract

We present a refined, improved $L^2$ -theory for the $\bar{\partial}$ -operator for $(0,q)$ and $(n,q)$ -forms on Hermitian complex spaces of pure dimension $n$ with isolated singularities. The general philosophy is to use a resolution of singularities to obtain a regular model of the $L^2$ -cohomology.

Keywords

operator theory cohomology theory operator theory and elliptic operators

Cite

@article{arxiv.1110.2373,
  title  = {$L^2$-theory for the $\bar{\partial}$-operator on complex spaces with isolated singularities},
  author = {Jean Ruppenthal},
  journal= {arXiv preprint arXiv:1110.2373},
  year   = {2015}
}

Comments

34 pages

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