# A Dolbeault-Hilbert complex for a variety with isolated singular points

## TL;DR

This paper develops a Dolbeault-Hilbert complex for complex spaces with isolated singularities, linking analytic and algebraic cohomology theories and connecting to Baum-Fulton-MacPherson's K-homology class.

## Contribution

It introduces a Dolbeault-type Hilbert complex for singular complex spaces and establishes its cohomology's isomorphism with the structure sheaf's cohomology.

## Key findings

- Constructed a Dolbeault-Hilbert complex for singular spaces
- Proved the cohomology is isomorphic to the structure sheaf's cohomology
- Connected the complex's K-homology class to Baum-Fulton-MacPherson's class

## Abstract

Given a compact Hermitian complex space with isolated singular points, we construct a Dolbeault-type Hilbert complex whose cohomology is isomorphic to the cohomology of the structure sheaf. We show that the corresponding K-homology class coincides with the one constructed by Baum-Fulton-MacPherson.