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

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.

This paper has been withdrawn by the author.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

References in corpus (1)

• $L^2$-Riemann-Roch for singular complex curves