Stability conditions for the local projective plane
Seminar Room 1, Newton Institute
Describing the space of Bridgeland stability conditions for the local projective plane turns out to be intimately related to classical results by Drezet and Le Potier on inequalities for Chern classes of slope-stable vector bundles on P2. I will describe how this allows one to relate the geometry of this space, and the group of autoequivalences, to the congruence subgroup Gamma1(3). I will also explain a mirror symmetry statement involving the moduli space of elliptic curves with Gamma1(3)-level structure.
Time permitting, I will also discuss observations on the same problem for local del Pezzo surfaces. This is based on joint work with Emanuele Macrì.