Minimal free resolutions and the arithmetical rank of Stanley-Reisner ideals

点击翻译按钮获取中文摘要

We studied the arithmetical rank of Stanly-Reisner ideals, which are squarefree monomial ideals in a polynomial ring. It is known that the arithmetical rank of a Stanley-Reisner ideal is greater than or equal to the projective dimension of the Stanley-Reisner ring, which is the length of the minimal free resolutions of the quotient ring. As for the edge ideal of a forest, Barile conjectures that these numbers will be coincident. We proved it. As for a Gorenstein Stanly-Reisner ideal of height three, we proved that its arithmetical rank is equal to the projective dimension of the Stanly-Reisner ring, too.