Now showing items 1-3 of 3

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

      Jeffries, J.; Nakajima, Y.; Smirnov, I.; Watanabe, K.; Yoshida, K. (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 

      Ma, L.; Smirnov, I. (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 

      Ma, L.; Smirnov, I. (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, ...