Lech's Inequality for the Buchsbaum-Rim Multiplicity and Mixed Multiplicity

2019/12/02 by Nguyen, Vinh, Walters, Kelsey
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.01073

Abstract

We generalize an improved Lech bound, due to Huneke, Smirnov, and Validashti, for 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.

Related

• A generalization of an inequality of Lech relating multiplicity and colength
• Mixed Buchsbaum--Rim Multiplicities
• Asymptotic Lech's inequality
• Lech's conjecture in dimension three
• A Note on the Buchsbaum-Rim multiplicity of a parameter module