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

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

1997-11-03

arxiv.org/abs/alg-geom/9711003v1

Mathematics

Algebraic Geometry

53 pages, amstex

Scientific paper

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.

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