Stability conditions on K3 surfaces via mass of spherical objects

Abstract

We prove that a stability condition on a K3 surface is determined by the masses of spherical objects up to a natural $\mathbb{C}$-action. This is motivated by the result of Huybrechts and the recent proposal of Bapat-Deopurkar-Licata on the construction of a compactification of a stability manifold. We also construct lax stability conditions in the sense of Broomhead-Pauksztello-Ploog-Woolf associated to spherical bundles.