F-Volumes
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, I1, …, It. 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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