$F$-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 $J$, $c^J(I)$ to a sequence of ideals $J$, $I_1,\dots ,I_t$. 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.

20 pages

References in corpus (3)

• Two theorems about maximal Cohen--Macaulay modules
• F-thresholds and Bernstein-Sato polynomials
• F-signature exists

Cited by in corpus (1)

• $F$-pure thresholds and $F$-Volumes of some non principal ideals