Pure Hodge structure on the $L_2$-cohomology of varieties with isolated singularities

Abstract

Let $V$ be a complex projective variety with isolated singularities. Let the smooth part be given the metric induced by a projective imbedding. Then we develop the $L_2$ harmonic theory and construct a pure Hodge structure on the $L_2$-cohomology of $V$. If the dimension of $V$ is two, we put a cohomological Hodge structure on its complex of sheaves of $L_2$ forms.

arXiv comment53 pages, amstex

References in corpus (1)

• Pure Hodge structure on the $L_2$-cohomology of varieties with isolated singularities

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