Lech's inequality, the Stückrad--Vogel conjecture, and uniform behavior of Koszul homology

Patricia Klein, Linquan Ma, Pham Hung Quy +2

Let $(R,\mathfrak{m})$ be a Noetherian local ring, and let $M$ be a finitely generated $R$-module of dimension $d$. We prove that the set $\left\{\frac{l(M/IM)}{e(I, M)} \right\}_{…