The Space of Stability Conditions on the Projective Plane

Abstract

The space of Bridgeland stability conditions on the bounded derived category of coherent sheaves on P2 has a principle connected component Stab^†(P2). We show that Stab^†(P2) is the union of geometric and algebraic stability conditions. As a consequence, we give a cell decomposition for Stab^†(P2) and show that Stab^†(P2) is contractible.

19 pages, comments are very welcome