$L^2$-sheaves of holomorphic functions and $n$-forms on complex spaces with isolated singularities

Jean Ruppenthal

$L^2$-sheaves of holomorphic functions and $n$-forms on complex spaces with isolated singularities

Complex Variables 2015-01-19 v2 Algebraic Geometry

Authors: Jean Ruppenthal

Abstract

Let $X$ be a Hermitian complex space of pure dimension $n$ with isolated singularities. In the present paper, we give a natural resolution for the canonical sheaf of square-integrable holomorphic $n$ -forms with Dirichlet boundary condition on $X$ . As application, we obtain an explicit smooth model for the $L^2$ - $\bar{\partial}$ -cohomology, including natural resolutions for sheaves of $\bar{\partial}$ -closed (holomorphic) $L^2$ -functions.

Keywords

hermitian complex space isolated singularities l2 sheaves holomorphic n-forms dirichlet boundary condition l2-barpartial-cohomology

Cite

@article{arxiv.1501.00584,
  title  = {$L^2$-sheaves of holomorphic functions and $n$-forms on complex spaces with isolated singularities},
  author = {Jean Ruppenthal},
  journal= {arXiv preprint arXiv:1501.00584},
  year   = {2015}
}

Comments

This paper has been withdrawn by the author. There is a mistake in the proof of Theorem 1.1, it is unclear whether this can be fixed

$L^2$-sheaves of holomorphic functions and $n$-forms on complex spaces with isolated singularities

Abstract

Keywords

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