Epsilon multiplicity for graded algebras |
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| Authors: | Suprajo Das |
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| Affiliation: | 1. Statistics and Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700 108, India;2. Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Prayagraj (Allahabad) 211 019, India;1. School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom;2. Department of Mathematics, University of Manchester, Oxford Road M13 6PL, United Kingdom;1. Department of Mathematics, The University of Uath, Salt Lake City, UT 84112, USA;2. Google LLC, 1600 Amphitheater Parkway, Mountain View, CA, USA |
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| Abstract: | The notion of ε-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 ε-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 ε-multiplicity, as corollaries of our main theorem. |
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| Keywords: | 14C99 13H05 52B20 13A02 13D45 |
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