The Multivariate Fundamental Theorem of Algebra and Algebraic Geometry
Algebraic Geometry
2007-05-23 v1 Commutative Algebra
Abstract
We derive two consequences of the multivariate fundamental theorem of algebra (MFTA). The first one is the Bezout theorem for polynomials. Notably the intersection multiplicities, as in MFTA, are characterized just by means of partial differential operators given by polynomials from -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.
Cite
@article{arxiv.math/0403460,
title = {The Multivariate Fundamental Theorem of Algebra and Algebraic Geometry},
author = {H. Hakopian},
journal= {arXiv preprint arXiv:math/0403460},
year = {2007}
}