The stability manifold of local orbifold elliptic quotients

Abstract

In this paper, we investigate the stability manifold of local models of orbifold quotients of elliptic curves. In particular, we describe a component of the stability manifold which maps as a covering space onto the universal unfolding space of the mirror singularity. The construction requires a detailed study of the McKay correspondence for $A_N$ surface singularities and a study of wall-crossing phenomena.

V2: 29 pages, added Lemma 5.13 to fill a gap in the argument, no result is affected. Comments are welcome! V3: 32 pages, main results now stated for normalized stability conditions. Several improvements under referee suggestions. To appear in J. London Math. Soc

References in corpus (1)

• MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations