The Multivariate Fundamental Theorem of Algebra and Algebraic Geometry

2004/03/26 by H. Hakopian
Mathematics · #math.AG #math.AC #msc:14C17 #msc:13H15 #msc:13F20

paper · pdf

published as MEGA 2003, International Conference, Short Communications, Kaiserslautern, Germany (2003)

arxiv created 2004/03/26 · arxiv updated 2009/12/01

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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