The effective cone of the moduli space of sheaves on the plane
  We compute the cone of effective divisors on any moduli space of semistable sheaves on the plane. The computation hinges on finding a good resolution of a general stable sheaf. 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. 
Izzet Coskun, Jack Huizenga, and Matthew Woolf
math.AG math.NT