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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 1997
- DOI:
- 10.48550/arXiv.alg-geom/9711003
- arXiv:
- arXiv:alg-geom/9711003
- Bibcode:
- 1997alg.geom.11003P
- Keywords:
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- Algebraic Geometry;
- Differential Geometry;
- Mathematics - Algebraic Geometry;
- Mathematics - Differential Geometry
- E-Print:
- 53 pages, amstex