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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.
32C25 Analytic subsets and submanifolds
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
32B05 Analytic algebras and generalizations, preparation theorems
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