The Minimal Model Program for moduli spaces of sheaves on K3 surfaces (Macrì)
In these lectures I will present joint work with Arend Bayer
(arXiv:1203.4613 and arXiv:1301.6968).
(1) The Positivity Lemma. Given a Bridgeland stability condition, I
will motivate and explain how to naturally associate a nef divisor on
the moduli space of Bridgeland stable objects.
(2) Explicit wall-crossing for K3 surfaces. I will explain
projectivity of moduli spaces of stable objects for K3s, and relate
concrete wall-crossing to concrete geometry (e.g., Brill-Noether loci,
relation to existence of g^1_n on curves in the case of the Hilbert
(3) Systematic wall-crossing analysis for K3 surfaces in terms of its
lattice and applications. I will describe of the nef cone of the
moduli spaces in terms of the K3 lattice.
If time permits, I will also talk about Lagrangian fibrations, and
more systematic examples.