L2-theory for the dbar-operator on compact complex spaces

Details L2-theory for the dbar-operator on compact complex spaces L2-theory for the dbar-operator on compact complex spaces

2010-04-02

arxiv.org/abs/1004.0396v1

Mathematics

Complex Variables

39 pages

Scientific paper

In the 1960s, the L2-theory for the dbar-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 L2-theory for the dbar-operator on singular complex spaces. In the present article, we make some steps towards such a theory for (0,q) and (n,q)-forms on compact complex spaces of pure dimension n with isolated singularities. Some of our methods apply to arbitrary singularities and non-compact situations, as well.

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