The minimal free resolution of a class of square-free monomial ideals

Abstract

AbstractFor positive integers n,b1⩽b2⩽⋯⩽bn and t⩽n, let It be the transversal monomial ideal generated by square-free monomials (∗)yi1j1yi2j2⋯yitjt,1⩽i1<i2<⋯<it⩽n,1⩽jk⩽bik,k=1,…,t,where yij's are distinct indeterminates. It is observed that the simplicial complex associated to this ideal is pure shellable if and only if b1=⋯=bn=1, but its Alexander dual is always pure and shellable. The simplicial complex admits some weaker shelling which leads to the computation of its Hilbert series. The main result is the construction of the minimal free resolution for the quotient ring of It. This class of monomial ideals includes the ideals of t-minors of generic pluri-circulant matrices under a change of coordinates. The last family of ideals arise from some specializations of the defining ideals of generic singularities of algebraic varieties