A Dolbeault-Grothendieck lemma on complex spaces via Koppelman formulas

• 成果类型: Article
• 署名作者: Andersson, Mats; Samuelsson, Hakan
• 署名单位: Chalmers University of Technology; University of Gothenburg
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0380-9
• 发表日期: 2012
• 页码: 261-297
• 关键词: integral-representation; differential forms; analytic spaces; VARIETIES; (partial-derivative)over-bar; RESOLUTIONS; THEOREM

摘要

Let X be a complex space of pure dimension. We introduce fine sheaves of (0,q)-currents, which coincides with the sheaves of smooth forms on the regular part of X, so that the associated Dolbeault complex yields a resolution of the structure sheaf . Our construction is based on intrinsic and quite explicit semi-global Koppelman formulas.