Mixed multiplicities and projective degrees of rational maps
Yairon Cid Ruiz
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Submission date: 05. Jan. 2020
MSC-Numbers: 13H15, 14E05
Link to arXiv: See the arXiv entry of this preprint.
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.