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$F$-Volumes (1912.03710v2)
Published 8 Dec 2019 in math.AC
Abstract: In this work we define a numerical invariant called $F$-volume. This number extends the definition of $F$-threshold of a pair of ideals $I$ and $J$, $cJ(I)$ to a sequence of ideals $J$, $I_1, \ldots, I_t$. We obtain several properties that emulate those of the $F$-threshold. In particular, the $F$-volume detects $F$-pure complete intersections. In addition, we relate this invariant to the Hilbert-Kunz multiplicity.
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