计算algebraic geometry中的Casas-Alvero猜想
Casas-Alvero conjecture in computational algebraic geometry
摘要：
我们通过计算代数几何的方法，特别是依靠组合零点和Noether规范化的衍生物的参数化多项式定义的品种。我们建立了这些多项式容易形成正则序列。这使我们能够计算这样定义的品种的维数，从而证明了Casas-Alvero猜想。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
