Abstract
We extend the asymptotic Samuel function of an ideal to a filtration and show that many of the good properties of this function for an ideal are true for filtrations. There are, however, interesting differences, which we explore. We study the notion of projective equivalence of filtrations and the relation between the asymptotic Samuel function and the multiplicity of a filtration. We further consider the case of discrete valued filtrations and show that they have particularly nice properties.
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The first author was partially supported by NSF grant DMS-2054394.
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Dedicated to Ngo Viet Trung on the occasion of his seventieth birthday.
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Cutkosky, S.D., Praharaj, S. The Asymptotic Samuel Function of a Filtration. Acta Math Vietnam (2024). https://doi.org/10.1007/s40306-024-00523-x
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DOI: https://doi.org/10.1007/s40306-024-00523-x