The membership problem for polynomial ideals in terms of residue currents (Q818300)
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| English | The membership problem for polynomial ideals in terms of residue currents |
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The membership problem for polynomial ideals in terms of residue currents (English)
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24 March 2006
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A relation between the vanishing of a globally defined residue current on \(\mathbb{P}^n\) and solution of the membership problem with control of the polynomial degree is revealed in this paper. Several classical results are deduced as its special cases, such as Max-Noether's theorem with a generalization. Furthermore there are some connections to an effective versions of the Nullstellensatz. Finally explicit integral representations of the solutions are presented.
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membership problem
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polynomial ideal
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residue current
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integral representations
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