Alexander duality for the alternative polarizations of strongly stable ideals

摘要

We will define the Alexander duality for strongly stable ideals. More precisely, for a strongly stable ideal with for all its dual is a strongly stable ideal with for all This duality has been constructed by Floystad et al.in a different manner, so we emphasis applications here. For example, we will describe the Hilbert series of the local cohomologies using the irreducible decomposition of I (through the Betti numbers of I*).