Mathematics – Algebraic Geometry
Scientific paper
2012-03-20
Mathematics
Algebraic Geometry
50 pages. Comments welcome
Scientific paper
We construct a family of nef divisor classes on every moduli space of stable complexes in the sense of Bridgeland. This divisor class varies naturally with the Bridgeland stability condition. For a generic stability condition on a K3 surface, we prove that this class is ample, thereby generalizing a result of Minamide, Yanagida, and Yoshioka. Our result also gives a systematic explanation of the relation between wall-crossing for Bridgeland-stability and the minimal model program for the moduli space. We give three applications of our method for classical moduli spaces of sheaves on a K3 surface: 1. We obtain a region in the ample cone in the moduli space of Gieseker-stable sheaves only depending on the lattice of the K3. 2. We determine the nef cone of the Hilbert scheme of n points on a K3 surface of Picard rank one when n is large compared to the genus. 3. We verify the "Hassett-Tschinkel/Huybrechts/Sawon" conjecture on the existence of a birational Lagrangian fibration for the Hilbert scheme in a new family of cases.
Bayer Arend
Macri Emanuele
No associations
LandOfFree
Projectivity and Birational Geometry of Bridgeland moduli spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Projectivity and Birational Geometry of Bridgeland moduli spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Projectivity and Birational Geometry of Bridgeland moduli spaces will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-487755