The ample cone of moduli spaces of sheaves on the plane

Let ξ be the Chern character of a stable sheaf on P². Assume either rk(ξ) ≤ 6 and that there are no strictly semistable sheaves with character ξ, or that rk(ξ) and c₁(ξ) are coprime and the discriminant Δ(ξ) is suffciently large. We use recent results of Bayer and Macrìon Bridgeland stability to compute the ample cone of the moduli space M(ξ) of Gieseker-semistable sheaves on P². We recover earlier results, such as those by Strømme and Yoshioka, as special cases.