Resolution of ideals associated to subspace arrangements

Given a subspace arrangement we may associate to it two ideals, the intersection of the linear ideals associated to each subspace or their product. The structure of the intersection ideal is mostly unknown. For example already for a finite collection of generic points in a projective space the degree of the generators of the intersection is not known. On the other hand the product ideal is better understood. An old theorem of Herzog and myself asserts that the product ideal has a linear resolution, or, which is the same, its regularity is given by the number of factors. In the talk we will discuss the structure of the resolution of the product ideal. We will see that such a resolution is supported on a polymatroid.

In collaboration with Manolis Tsakiris of ShanghaiTech.