Duality, Bridgeland wall-crossing and flips of secant varieties

Abstract

Let $v_d(\mathbb{P}^2)\subset |\mathcal{O}_{\mathbb{P}^2}(d)|$ denote the $d$-uple Veronese surface. After studying some general aspects of the wall-crossing phenomena for stability conditions on surfaces, we are able to describe a sequence of flips of the secant varieties of $v_d(\mathbb{P}^2)$ by embedding the blow-up $\mbox{bl}_{v_d(\mathbb{P}^2)}|\mathcal{O}_{\mathbb{P}^2}(d)|$ into a suitable moduli space of Bridgeland semistable objects on $\mathbb{P}^2$.