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- W2886873708 abstract "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 $left{frac{l(M/IM)}{e(I, M)} right}_{sqrt{I}=mathfrak{m}}$ is bounded below by ${1}/{d!e(overline{R})}$ where $overline{R}=R/Ann(M)$. Moreover, when $widehat{M}$ is equidimensional, this set is bounded above by a finite constant depending only on $M$. The lower bound extends a classical inequality of Lech, and the upper bound answers a question of St{u}ckrad--Vogel in the affirmative. As an application, we obtain results on uniform behavior of the lengths of Koszul homology modules." @default.
- W2886873708 created "2018-08-22" @default.
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- W2886873708 date "2019-04-01" @default.
- W2886873708 modified "2023-10-18" @default.
- W2886873708 title "Lech's inequality, the Stückrad–Vogel conjecture, and uniform behavior of Koszul homology" @default.
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- W2886873708 doi "https://doi.org/10.1016/j.aim.2019.02.029" @default.
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