论文标题
过滤的Minkowski平等
The Minkowski Equality for Filtrations
论文作者
论文摘要
假设R是具有最大理想M_R的分析性不可约或出色的本地域。我们考虑通过M_R主要理想的过滤来考虑R的多重性和混合多重性。我们表明，Teissier，Rees和Sharp的定理以及Katz的定理，表征了Minkowski不平等中的平等，对于理想的多重性，对于分区过滤是正确的，对于较大的有限过滤。对于M_R基理想的任意过滤，该定理不是正确的。
Suppose that R is an analytically irreducible or excellent local domain with maximal ideal m_R. We consider multiplicities and mixed multiplicities of R by filtrations of m_R-primary ideals. We show that the theorem of Teissier, Rees and Sharp, and Katz, characterizing equality in the Minkowski inequality for multiplicities of ideals, is true for divisorial filtrations, and for the larger category of bounded filtrations. This theorem is not true for arbitrary filtrations of m_R-primary ideals.
