On the L"2-stokes theorem and hodge theory for ingular algebraic varieties

We discuss aspects of the L"2-Stokes theorem on certain manifolds with singularities. We show that the L"2-Stokes theorem does not hold on real projective varietes, even for isolated singularities. For a complex projective variety of complex dimension n, with isolated singularities, we show that the Laplacians of the de Rham and Dolbeault complexes are discrete operators except possibly in degrees n,n#+-#1. A consequence is a Hodge theorem on the operator level as well as the fact that the L"2-Stokes theorem holds except possibly in degrees n-1, n. However, in general the conjecture that the L"2-Stokes theorem holds on complex projective varieties remains still open. (orig.)Available from TIB Hannover: RR 1596(369) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman