Jack Huizenga

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.

The ample cone of moduli spaces of sheaves on the plane

Fix a Chern character of a stable sheaf on the plane. Assume either the rank is at most 6 or the rank and first Chern class are coprime and the discriminant is sufficiently large. We use recent results of Bayer and Macri on Bridgeland stability to compute the ample cone of the moduli space of Gieseker semistable sheaves with the given Chern character. We recover earlier results, such as those by Stromme and Yoshioka, as special cases.