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Degree of a polynomial ideal and Bézout inequalities

Abstract : A complete theory of the degree of a polynomial ideal is presented, with a systematic use of the rational form of the Hilbert function in place of the (more commonly used) Hilbert polynomial. This is used for a simple algebraic proof of classical Bézout theorem, and for proving a "strong Bézout inequality", which has as corollaries all previously known Bézout inequalities , and is much sharper than all of them in the case of a non-equidimensional ideal.
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Contributor : Daniel Lazard <>
Submitted on : Sunday, July 12, 2020 - 11:53:52 AM
Last modification on : Tuesday, March 23, 2021 - 9:28:03 AM
Long-term archiving on: : Monday, November 30, 2020 - 9:24:55 PM


Bezout draft.pdf
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  • HAL Id : hal-02897419, version 1


Daniel Lazard. Degree of a polynomial ideal and Bézout inequalities. 2020. ⟨hal-02897419⟩



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