On Bernstein-Sato ideals for central line arrangements

The polynomial alpha=xy Pi(m)(i=3)(a(i)x+y)is an element of C[x,y] determines a plane central line arrangement alpha = 0. We compute explicitly multivariate Bernstein-Sato ideals of alpha by using the decomposition behavior of the D-2-module M-alpha(beta)=C[x,y,1/alpha]alpha(beta) given in earlier work by the authors. Our results are partially special cases of recent work in much greater generality, by Maisonobe on free hyperplane arrangements and Budur et al.) as well as Bath; however our proof is independent and gives some more information on different variants of Bernstein-Sato ideals in the simple plane case.