The effective cone of the moduli space of sheaves on the plane

Let ζ be the Chern character of a stable coherent sheaf on P2. We compute the cone of effective divisors on the moduli space M(ζ) of semistable sheaves on P2 with Chern character ζ. The computation hinges on finding a good resolution of the general sheaf inM(ζ). This resolution is determined by Bridgeland stability and arises from a well-chosen Beilinson spectral sequence. The existence of a good choice of spectral sequence depends on remarkable number-theoretic properties of the slopes of exceptional bundles.