In the need of computational tools for epsilon-multiplicity, we provide a criterion for a module with a rank E inside a free module F to have rational epsilon-multiplicity in terms of the finite generation of the saturation Rees algebra of E. In this case, the multiplicity can be related to a Hilbert multiplicity of certain graded algebra. A particular example of this situation is provided: it is shown that the epsilon-multiplicity of monomial modules is Noetherian. Numerical evidence is provided that leads to a conjecture formula for the epsilon-multiplicity of certain monomial curves in the 3-affine space.
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/12735638 |
| Date | 29 July 2020 |
| Creators | Roberto Antonio Ulloa-Esquivel (9183071) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/Epsilon_multiplicity_of_modules_with_Noetherian_saturation_algebras/12735638 |
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