Moduli Spaces of $\alpha$-stable Pairs and Wall-Crossing on ${\mathbb{P}}^2$

Jinwon Choi, Kiryong Chung

We study the wall-crossing of the moduli spaces ${\mathbf{M}}^{\alpha }(d,1)$ of $\alpha$-stable pairs with linear Hilbert polynomial $dm+1$ on the projective plane ${\mathbb{P}}^2$ as we alter the…