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Mixed multiplicities and projective degrees of rational maps
Journal of Algebra ( IF 0.9 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.jalgebra.2020.08.037
Yairon Cid-Ruiz

We consider the notion of mixed multiplicities for multigraded modules by using Hilbert series, and this is later applied to study the projective degrees of rational maps. We use a general framework to determine the projective degrees of a rational map via a computation of the multiplicity of the saturated special fiber ring. As specific applications, we provide explicit formulas for all the projective degrees of rational maps determined by perfect ideals of height two or by Gorenstein ideals of height three.

中文翻译:

有理映射的混合多重性和投影度

我们使用希尔伯特级数考虑了多级模块的混合多重性概念,这后来被应用于研究有理映射的射影度。我们使用通用框架通过计算饱和特殊纤维环的多重性来确定有理映射的投影度。作为具体应用,我们为由高度二的完美理想或高度三的 Gorenstein 理想确定的所有有理映射的投影度提供了明确的公式。
更新日期:2021-01-01
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