标题： 实向量场在孤立完全交奇点处的指标 显示英文标题

标题： The index of a real vector field at an isolated complete intersection singularity

摘要： 在未发表的笔记[H1]中，我们描述了一种方法，以获得在具有（复数）孤立奇点的实解析超曲面上具有（复数）孤立零点的解析向量场的指标公式。 此公式类似于Eisenbud-Levine和Khimshiashvili[AGV]对光滑点的公式，通过局部余数符号定义的双线性形式的符号来表示指标（参见[Ma]）。 在完全交情况下，我们使用了在[ LJ ]中为自由分解定义的广义余数符号，在广义Koszul复形的特殊情况下，以获得涉及双线性形式的适当计算方法。 显示英文摘要

摘要： In an unpublished note [H1] we have described a method to obtain a formula for the index of an analytic vector field with (complex) isolated zero on a real analytic hypersurface with (complex) isolated singularity. This formula, like the one of Eisenbud-Levine and Khimshiashvili [AGV] for smooth points, expresses the index by the signature of bilinear forms, which are defined by a local residue symbol (cf. [Ma]). In the complete intersection case, we use a generalized residue symbol, defined for free resolutions in [LJ], in the special case of generalized Koszul complexes to obtain a suitable calculus for the bilinear forms involved.