Invariant stability conditions on local ${\mathbb{P}}^1\times {\mathbb{P}}^1$ (after Del Monte-Longhi)

Abstract

Let $X$ be the total space of canonical bundle of $\pp$, we study an invariant subspace of stability conditions on $X$ under an autoequivalence of $D^b(X)$. We describe the complete set of stable objects with respect to the invariant stability conditions and characterize the space of invariant stability conditions.

arXiv commentpublished version, to appear in Journal of Algebra