Resolution of ideals associated to subspace arrangements

Let J be the product of n ideals generated by linear forms in a polynomial ring. We describe a minimal free resolution of J and show that it is supported on a polymatroid obtained from the underlying representable polymatroid by means of the so-called Dilworth truncation. Formulas for the projective dimension and Betti numbers are given in terms of the polymatroid as well as a characterization of the associated primes.