论文标题
通过全球维度功能在投影平面上稳定空间的合同性
Contractibility of space of stability conditions on the projective plane via global dimension function
论文作者
论文摘要
我们计算主组件$ \ mathrm {stab}^†（\ Mathbb {p}^2）$ \ m athbb {p}^2 $上的全局尺寸函数$ \ mathrm {gldim} $在Bridgeland稳定条件上的主稳定性条件的空间的主组件$ \ Mathrm {stab}^†（\ Mathbb {p}^2）$。它承认$ 2 $作为最小值和预映率$ \ mathrm {gldim}^{ - 1}（2）$包含在闭合$ \ bar {\ mathrm {stab}^{\ mathrm {\ mathrm {geo}}}（geo}}（geo}}}（\ mathbb {p} p}^2）$的情况下，我们表明$ \ mathrm {gldim}^{ - 1} [2，x）$合同到$ \ mathrm {gldim}^{ - 1}^{ - 1}（2）$对于任何实际数字$ x \ geq 2 $，该$ x \ geq 2 $，the $ \ \ mathrm {gldim}^gldim}^{ - 1} { - 1}（2）（2）$是合同。
We compute the global dimension function $\mathrm{gldim}$ on the principal component $\mathrm{Stab}^†(\mathbb{P}^2)$ 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 $\mathrm{gldim}^{-1}[2,x)$ contracts to $\mathrm{gldim}^{-1}(2)$ for any real number $x\geq 2$ and that $\mathrm{gldim}^{-1}(2)$ is contractible.
