The Multivariate Fundamental Theorem of Algebra and Algebraic Geometry

H. Hakopian

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arXiv · math/0403460

The Multivariate Fundamental Theorem of Algebra and Algebraic Geometry

H. Hakopian

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Abstract

We derive two consequences of the multivariate fundamental theorem of algebra (MFTA). The first one is the Bezout theorem for $n$ polynomials. Notably the intersection multiplicities, as in MFTA, are characterized just by means of partial differential operators given by polynomials from $D$-invariant linear spaces. The second consequence provides a solution to the ideal membership problem, based on the above characterization of intersection multiplicities. Let us mention that one readily gets Nullstellensatz from here.

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H. Hakopian. 2004-03-26. The Multivariate Fundamental Theorem of Algebra and Algebraic Geometry. https://arxiv.org/abs/math/0403460

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