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On the characterization of Alexander schemes. (English) Zbl 0831.14001
Alexander schemes form the firm foundation for a study of the Chow group. The author defines a notion of Alexander scheme equivalent to that of A. Vistoli on connected components. Furthermore, it becomes clear from the definition that Alexander schemes are the most general natural class of schemes which behave like smooth schemes for intersection theory. A practical criterion for deciding whether a given scheme is Alexander is given. A natural extension from Alexander scheme to Alexander morphism is made. Finally, using the tools developed, conditions defining whether a cone over a smooth projective variety is Alexander are found.

MSC:
14C05 Parametrization (Chow and Hilbert schemes)
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
14A15 Schemes and morphisms
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References:
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