Contractibility of space of stability conditions on the projective plane via global dimension function

31 Jan 2020Yu-Wei FanChunyi LiWanmin LiuYu Qiu

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 $\mathbb{P}^2$. We describe the preimage $\mathrm{gldim}^{-1}(2)$ of the minimal value $2$ of $\mathrm{gldim}$, which is contained in the closure $\overline{\mathrm{Stab}^{\mathrm{Geo}}(\mathbb{P}^2)}$ of the subspace consisting of geometric stability conditions... (read more)

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