Componentwise linear ideals

A componentwise linear ideal is a graded ideal I of a polynomial ring such that, for each degree q, the ideal generated by all homogeneous polynomials of degree q belonging to I has a linear resolution. Examples of componentw ise linear ideals include stable monomial ideals and Gotzmann ideals. The g raded Betti numbers of a componentwise linear ideal can be determined by th e graded Betti numbers of its components. Combinatorics on squarefree compo nentwise linear ideals will be especially studied. It turns out that the St anley-Reisner ideal I-Delta arising from a simplicial complex Delta is comp onentwise linear if and only if the Alexander dual of a is sequentially Coh en-Macaulay. This result generalizes the theorem by Eagon and Reiner which says that the Stanley-Reisner ideal of a simplicial complex has a linear re solution if and only if its Alexander dual is Cohen-Macaulay.