L 2-partial derivative-Cohomology groups of some singular complex spaces

• 成果类型: Article
• 署名作者: Ovrelid, Nils; Vassiliadou, Sophia
• 署名单位: University of Oslo; Georgetown University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0414-3
• 发表日期: 2013
• 页码: 413-458
• 关键词: relative vanishing theorems; partial-derivative-equation; rational-singularities; VARIETIES; (partial-derivative)over-bar; l2-cohomology; COHOMOLOGY; extension; sheaf

摘要

Let X be a pure n-dimensional (where na parts per thousand yen2) complex analytic subset in a, (N) with an isolated singularity at 0. In this paper we express the L (2)-(0,q)--cohomology groups for all q with 1a parts per thousand currency signqa parts per thousand currency signn of a sufficiently small deleted neighborhood of the singular point in terms of resolution data. We also obtain identifications of the L (2)-(0,q)--cohomology groups of the smooth points of X, in terms of resolution data, when X is either compact or an open relatively compact complex analytic subset of a reduced complex space with finitely many isolated singularities.