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Mixed multiplicities and projective degrees of rational maps. (English) Zbl 07268487
Summary: 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.
MSC:
13H15 Multiplicity theory and related topics
14E05 Rational and birational maps
13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
13D02 Syzygies, resolutions, complexes and commutative rings
Software:
Macaulay2
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