Residue currents with prescribed annihilator ideals
نویسندگان
چکیده
منابع مشابه
Ideals of Smooth Functions and Residue Currents
Let f = (f 1 ; : : : ; f m) be a holomorphic mapping in a neighborhood of the origin in C n. We nd suucient condition, in terms of residue currents, for a smooth function to belong to the ideal in C k generated by f. If f is a complete intersection the condition is essentially necessary. More generally we give suucient condition for an element of class C k in the Koszul complex induced by f to ...
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A right ideal A of a ring R is called annihilator-small if A+ T = R; T a right ideal, implies that l(T ) = 0; where l( ) indicates the left annihilator. The sum Ar of all such right ideals turns out to be a two-sided ideal that contains the Jacobson radical and the left singular ideal, and is contained in the ideal generated by the total of the ring. The ideal Ar is studied, conditions when it ...
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We find a relation between the vanishing of a globally defined residue current on Pn and solution of the membership problem with control of the polynomial degrees. Several classical results appear as special cases, such as Max Nöther’s theorem, and we also obtain a generalization of that theorem. There are also connections to effective versions of the Nullstellensatz. We also provide explicit i...
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We deene a residue current of a holomorphic mapping , or more generally a holomorphic section to a holomorphic vector bundle, by means of Cauchy-Fantappie-Leray type formulas , and prove that a holomorphic function that annihilates this current belongs to the corresponding ideal locally. We also prove that the residue current coincides with the Colee-Herrera current in the case of a complete in...
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ژورنال
عنوان ژورنال: Annales Scientifiques de l’École Normale Supérieure
سال: 2007
ISSN: 0012-9593
DOI: 10.1016/j.ansens.2007.11.001