L–Theory for the ∂̄–Operator on Compact Complex Spaces

In the 1960s, the L-theory for the ∂-operator has become an important, indispensable part of complex analysis with influence to many other areas of mathematics. But, whereas the theory is very well developed on complex manifolds, it has been an open problem ever since to create an appropriate L-theory for the ∂-operator on singular complex spaces. In the present article, we develop such a theory for (0, q) and (n, q)-forms on compact complex spaces of pure dimension n with isolated singularities. Most of our methods apply to arbitrary singularities and non-compact situations, as well.