1 8 Fe b 20 09 COLEFF - HERRERA CURRENTS , DUALITY , AND NOETHERIAN OPERATORS
نویسنده
چکیده
Let J be a coherent subsheaf of a locally free sheaf O(E 0) and suppose that F = O(E 0)/J has pure codimension. Starting with a residue current R obtained from a locally free resolution of F we construct a vector-valued Coleff-Herrera current µ with support on the variety associated to F such that φ is in J if and only if µφ = 0. Such a current µ can also be derived algebraically from a fundamental theorem of Roos about the bid-ualizing functor, and the relation between these two approaches is discussed. By a construction due to Björk one gets Noetherian operators for J from the current µ. The current R also provides an explicit realization of the Dickenstein-Sessa decomposition and other related canonical isomorphisms.
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