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Analytic deviation of ideals and intersection theory of analytic spaces. (English) Zbl 0802.32017
Let $$X$$ be a complex space and $$Z$$ a closed complex subspace defined by a sheaf $$I$$. For $$x\in Z$$ the authors consider the analytic spread $$s(I_ x)$$, the height $$ht(I_ x)$$ and the analytic deviation $$s(I_ x)- ht(I_ x)$$. They show that $$Z$$ is stratified by the analytic subsets ${\mathcal G}_ n(Z,X):= \{x\in Z: s(I_ x)- ht(I_ x)\geq n\}.$ The stratification is used to define embedded intersection components for an intersection of complex subspaces. The authors make a construction which enables them to define an intersection multiplicity for such components. In the case of projective spaces one gets relations to investigations of Fulton and Stückrad-Vogel.
The technics of the authors are these of commutative algebra and semianalytic Stein compacta.
##### MSC:
 32C25 Analytic subsets and submanifolds 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry 32B05 Analytic algebras and generalizations, preparation theorems
##### Keywords:
intersection theory; analytic deviation; stratification
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##### References:
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