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Casas-Alvero conjecture in computational algebraic geometry (1707.04754v6)
Published 15 Jul 2017 in math.AC
Abstract: We study varieties defined by parameterizing polynomials of derivatives through a computational algebro-geometric approach, especially relying on Combinatorial Nullstellensatz and Noether normalization. We establish that these polynomials form regular sequences easily. This allows us to calculate the dimension of thus defined varieties and consequently give a proof to the Casas-Alvero conjecture.