Contractibility of space of stability conditions on the projective plane via global dimension function
Contractibility of space of stability conditions on the projective plane via global dimension function
We compute the global dimension function $\mathrm{gldim}$ on the principal component $\mathrm{Stab}^{\dag}(\mathbb{P}^2)$ of the space of Bridgeland stability conditions on $\mathbb{P}^2$. It admits $2$ as the minimum value and the preimage $\mathrm{gldim}^{-1}(2)$ is contained in the closure $\bar{\mathrm{Stab}^{\mathrm{Geo}}(\mathbb{P}^2)}$ of the subspace consisting of geometric stability conditions. We show that $\mathrm{gldim}^{-1}[2,x)$ …