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• #### Lower bounds on Hilbert-Kunz multiplicities and maximal F-signature ﻿

(2022)
ABSTRACT. Hilbert–Kunz multiplicity and F-signature are numerical invariants of commutative rings in positive characteristic that measure severity of singularities: for a regular ring both invariants are equal to one and ...
• #### Uniform Lech's inequality ﻿

(2022)
Let (R,m) be a Noetherian local ring of dimension d ≥ 2. We prove that if e(R􏰊red) > 1, then the classical Lech’s inequality can be improved uniformly for all m-primary ideals, that is, there exists ε > 0 such that e(I) ...
• #### Uniform Lech's inequality ﻿

(2022)
Let (R,m) be a Noetherian local ring, and let M be a finitely generated R-module of dimension d. We prove that the set [Formula presented] is bounded below by 1/d!e(R‾) where R‾=R/Ann(M). Moreover, when Mˆ is equidimensional, ...