New paper: Ample stability implies rigidity for quiver moduli

Ample stability implies rigidity for quiver moduli (with Gianni Petrella) is a new paper that gets rid of an annoying technical condition in our earlier paper Rigidity and Schofield's partial tilting conjecture for quiver moduli (and subsequent papers building on the vanising results in this paper). Recall that, for a dimension vector $\mathbf{d}$ and a stability parameter $\theta$ with $\theta(\mathbf{d})=0$, we have the following three properties: Ample stability means that the complement of the stable locus in the space of representations of dimension $\mathbf{d}$ has codimension at least $2$. In this case the moduli space has maximal Picard rank: $\operatorname{rk}\operatorname{Pic}=\#Q_0-1$. The rigidity inequality asks that, for every nontrivial Harder–Narasimhan type $\mathbf{d}^*=(\mathbf{d}^1,\ldots,\mathbf{d}^\ell)$, where $\mu(\mathbf{e})=\theta(\mathbf{e})/|\mathbf{e}|$ denotes the slope, \[ \mu(\mathbf{d}^1)-\mu(\mathbf{d}^\ell) \lt \sum_{1\leq m\lt n\leq\ell}…