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arXiv · 1911.04531

Epsilon multiplicity for graded algebras

Suprajo Das
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Abstract

The notion of $\varepsilon$-multiplicity was originally defined by Ulrich and Validashti as a limsup and they used it to detect integral dependence of modules. It is important to know if it can be realized as a limit. In this article we show that the relative epsilon multiplicity of reduced standard graded algebras over an excellent local ring exists as a limit. We also obtain some important special cases of Cutkosky's results concerning $\varepsilon$-multiplicity, as corollaries of our main theorem.

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Suprajo Das. 2019-11-11. Epsilon multiplicity for graded algebras. https://arxiv.org/abs/1911.04531

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