19 citations · 56 across the 17 of their papers we have counts for
7 papers · 1 filter
The theory of F-rational signature
Ilya Smirnov, Kevin Tucker
F-signature is an important numeric invariant of singularities in positive characteristic that can be used to detect strong F-regularity. One would like to have a variant that rath…
Asymptotic Lech's inequality
Craig Huneke, Linquan Ma, Pham Hung Quy +1
We explore the classical Lech's inequality relating the Hilbert--Samuel multiplicity and colength of an -primary ideal in a Noetherian local ring .…
Filter regular sequence under small perturbations
Linquan Ma, Pham Hung Quy, Ilya Smirnov
We answer affirmatively a question of Srinivas--Trivedi: in a Noetherian local ring , if is an ideal generated by a filter-regular sequence an…
Colength, multiplicity, and ideal closure operations
Linquan Ma, Pham Hung Quy, Ilya Smirnov
In a formally unmixed Noetherian local ring, if the colength and multiplicity of an integrally closed ideal agree, then is regular. We deduce this using the relationship betwee…
Equimultiplicity Theory of Strongly -regular rings
Thomas Polstra, Ilya Smirnov
We explore the equimultiplicity theory of the -invariants Hilbert--Kunz multiplicity, -signature, Frobenius Betti numbers, and Frobenius Euler characteristic over strongly $F…
A transformation rule for natural multiplicities
Jack Jeffries, Ilya Smirnov
For multiplicities arising from a family of ideals we provide a general approach to transformation rules for a ring extension étale in codimension one. Our result can be applied to…
On semicontinuity of multiplicities in families
Ilya Smirnov
The paper investigates the behavior of Hilbert-Samuel and Hilbert-Kunz multiplicities in families of ideals. It is shown that Hilbert-Samuel multiplicity is upper semicontinuous al…