L2-theory for the dbar-operator on complex spaces with isolated singularities

Details L2-theory for the dbar-operator on complex spaces with isolated singularities L2-theory for the dbar-operator on complex spaces with isolated singularities

2011-10-11

arxiv.org/abs/1110.2373v1

Mathematics

Complex Variables

33 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 present such a theory for (0,q) and (n,q)-forms on complex spaces of pure dimension n with isolated singularities. The general philosophy is to use a resolution of singularities to obtain a regular model of the L2-cohomology.

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