论文标题
多边形，主要理想和非标准等级
Multidegrees, prime ideals, and non-standard gradings
论文作者
论文摘要
我们研究了多种均匀素数理想的几种特性。我们表明，素数具有非常特殊的特性，例如，其自由基是Cohen-Macaulay。我们在任意积极的多层环境中对多边形进行了全面研究。在这些环境中，我们通过标准化技术扩展了Cartwright-Sturmfels理想的概念。此外，我们在文献中恢复或扩展了重要的结果：我们提供了Hartshorne的结果的多边形版本，该版本在平坦的退化下说明了算术程度的上层半持续性，并且我们提供了Brion在多样性品种方面的替代证明。
We study several properties of multihomogeneous prime ideals. We show that the multigraded generic initial ideal of a prime has very special properties, for instance, its radical is Cohen-Macaulay. We develop a comprehensive study of multidegrees in arbitrary positive multigraded settings. In these environments, we extend the notion of Cartwright-Sturmfels ideals by means of a standardization technique. Furthermore, we recover or extend important results in the literature, for instance: we provide a multidegree version of Hartshorne's result stating the upper semicontinuity of arithmetic degree under flat degenerations, and we give an alternative proof of Brion's result regarding multiplicity-free varieties.
