Lech’s inequality for the Buchsbaum-Rim multiplicity and mixed multiplicity

Nguyen, Vinh; Walters, Kelsey

doi:10.1090/proc/15364

Lech’s inequality for the Buchsbaum-Rim multiplicity and mixed multiplicity
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by Vinh Nguyen and Kelsey Walters PDF

Proc. Amer. Math. Soc. 149 (2021), 1889-1904 Request permission

Abstract:

We generalize an improved Lech bound, due to Huneke, Smirnov, and Validashti, from the Hilbert-Samuel multiplicity to the Buchsbaum-Rim multiplicity and mixed multiplicity. We reduce the problem to the graded case and then to the polynomial ring case. There we use complete reductions, studied by Rees, to prove sharper bounds for the mixed multiplicity in low dimensions before proving the general case.

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