Roni Varshavsky
Title: Linear quotients, linear resolutions and the lcm-lattice
Abstract: Linear resolutions, and the stronger notion of linear quotients are interesting properties for monomial ideals. For squarefree monomial ideals, there is a natural simplicial complex associated to it via the Stanley-Reisner correspondance. Whether the monomial ideal has linear quotients or linear resolutions is fully characterized by combinatorial or homological properties of the Alexander dual of the associated simplicial complex. The lcm-lattice is another combinatorial structure associated with every monomial ideal (not necessarily squarefree). In this talk we will discuss a characterization for having linear quotients or linear resolutions in terms of the lcm-lattice as well, understanding better the relationship between the lcm-lattice and the Alexander dual of the simplicial complex associated to the monomial ideal in the squarefree case.
If time permits, we will discuss the private case of edge ideals as well, where we will see how the above characterization shows that the underlying graph is co-chordal if and only if the lcm-lattice is graded in a strong way and CL-shellable.