Ideals of smooth functions and residue currents
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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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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15 صفحه اولThe Membership Problem for Polynomial Ideals in Terms of Residue Currents
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Given a generically surjective holomorphic vector bundle morphism f : E → Q, E and Q Hermitian bundles, we construct a current R with values in Hom (Q,H), where H is a certain derived bundle, and with support on the set Z where f is not surjective. The main property is that if φ is a holomorphic section of Q, and Rφ = 0, then locally fψ = φ has a holomorphic solution ψ. In the generic case also...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2004
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2003.07.014