Abstract
Given Σ⊂R:=K[x1,…,xk], where K is a field of characteristic 0, any finite collection of linear forms, some possibly proportional, and any 1≤a≤|Σ|, we prove that Ia(Σ), the ideal generated by all a-fold products of Σ, has linear graded free resolution. This allows us to determine a generating set for the defining ideal of the Orlik-Terao algebra of the second order of a line arrangement in P2K, and to conclude that for the case k=3, and Σ defining such a line arrangement, the ideal I|Σ|−2(Σ) is of fiber type. We also prove several conjectures of symbolic powers for defining ideals of star configurations of any codimension c.