Purdue University Graduate School
Epsilon multiplicity of modules with Noetherian saturation algebras.pdf (378.97 kB)

Epsilon multiplicity of modules with Noetherian saturation algebras

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posted on 2020-07-29, 22:54 authored by Roberto Antonio Ulloa-EsquivelRoberto Antonio Ulloa-Esquivel
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.


Degree Type

  • Doctor of Philosophy


  • Mathematics

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Bernd Ulrich

Additional Committee Member 2

William Heinzer

Additional Committee Member 3

Giulio Caviglia

Additional Committee Member 4

Linquan Ma