$F$-Volumes
W\'agner Badilla-C\'espedes, Luis N\'u\~nez-Betancourt, Sandra, Rodr\'iguez-Villalobos
TL;DR
This paper introduces the $F$-volume, a new numerical invariant extending $F$-thresholds to sequences of ideals, which helps identify $F$-pure complete intersections and relates to Hilbert-Kunz multiplicity.
Contribution
The paper defines the $F$-volume, extending $F$-thresholds to sequences of ideals, and explores its properties and connections to other invariants.
Findings
$F$-volume detects $F$-pure complete intersections.
$F$-volume relates to Hilbert-Kunz multiplicity.
Properties of $F$-volume emulate those of $F$-threshold.
Abstract
In this work we define a numerical invariant called -volume. This number extends the definition of -threshold of a pair of ideals and , to a sequence of ideals , . We obtain several properties that emulate those of the -threshold. In particular, the -volume detects -pure complete intersections. In addition, we relate this invariant to the Hilbert-Kunz multiplicity.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic Geometry and Number Theory