2019/07/23 by Hirano, Yuki, Wemyss, Michael · 3 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.1907.09742
Let f\colon X\toSpec R be a 3-fold flopping contraction, where X has at worst Gorenstein terminal singularities and R is complete local. We describe the space of Bridgeland stability conditions on the null subcategory \mathscrC of the bounded derived category of X, which consists of those complexes that derive pushforward to zero, and also on the affine subcategory \mathscrD, which consists of complexes supported on the exceptional locus. We show that a connected component of stability conditions on \mathscrC is the universal cover of the complexified complement of the real hyperplane arrangement associated to X via the Homological MMP, and more generally that a connected component of normalised stability conditions on \mathscrD is a regular covering space of the infinite hyperplane arrangement constructed in Iyama-Wemyss [IW9]. Neither arrangement is Coxeter in general. As a consequence, we give the first description of the Stringy Kähler Moduli Space (SKMS) for all smooth irreducible 3-fold flops. The answer is surprising: we prove that the SKMS is always a sphere, minus either 3, 4, 6, 8, 12 or 14 points, depending on the length of the curve.