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The Multivariate Fundamental Theorem of Algebra and Algebraic Geometry | | H. Hakopian
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26 Mar 2004 | | Journal: | MEGA 2003, International Conference, Short Communications, Kaiserslautern, Germany (2003) | | Subject: | Algebraic Geometry; Commutative Algebra MSC-class: 14C17, 13H15, 13F20 | math.AG math.AC | | 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. | | Source: | arXiv, math.AG/0403460 | | Services: | Forum | Review | PDF | Favorites | |
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