Construction of stability conditions on some Kuznetsov components

Abstract

We construct Bridgeland stability conditions on the Kuznetsov components of smooth Fano hypersurfaces of degrees three, four, and six and dimension at least three, smooth quartic double fivefolds, and smooth Fano complete intersections of three quadrics. For odd-dimensional cubic hypersurfaces and quartic double fivefolds, every connected component of the numerical stability manifold is biholomorphic to $\mathbb C\times\mathbb H$. For general cubic sevenfolds and quartic double fivefolds, spherical twists produce infinitely many distinct connected components.