Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8895887 | Journal of Algebra | 2018 | 28 Pages |
Abstract
We define a function, called s-multiplicity, that interpolates between Hilbert-Samuel multiplicity and Hilbert-Kunz multiplicity by comparing powers of ideals to the Frobenius powers of ideals. The function is continuous in s, and its value is equal to Hilbert-Samuel multiplicity for small values of s and is equal to Hilbert-Kunz multiplicity for large values of s. We prove that it has an Associativity Formula generalizing the Associativity Formulas for Hilbert-Samuel and Hilbert-Kunz multiplicity. We also define a family of closures such that if two ideals have the same s-closure then they have the same s-multiplicity, and the converse holds under mild conditions. We describe the s-multiplicity of monomial ideals in toric rings as a certain volume in real space.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
William D. Taylor,