An inequality in mixed multiplicities

Abstract

The theory of mixed multiplicities of (not necessarily Noetherian) filtrations of $m_R$-primary ideals in a Noetherian local ring $R$, has been developed by Cutkosky, Sarkar and Srinivasan. The objective of this article is to generalise a Minkowski-type inequality given in their paper. We also recover a result of Cutkosky, Srinivasan and Verma as a simple consequence of our inequality.