论文标题
Uhlenbeck紧凑型作为Bridgeland Moduli空间
Uhlenbeck compactification as a Bridgeland moduli space
论文作者
论文摘要
令$（x，h）$为$ \ mathbb {c} $上的平滑，投射，两极分化的表面，让$ v \ in k _ {\ mathrm {num}}}（x）$是一类正等级。我们证明，对于某些Bridgeland稳定条件，$σ=（\ Mathcal {a}，z）$“在垂直墙上”，$ v $，良好的Moduli space $ m^σ（v）$参数化$σ$ - $σ$ semistable的$ v $类别$ v $ in $ \ nathcal in Chatcal的$σ$ qualivalence类别。 Moreover, we construct a bijective morphism $M^{\mathrm{Uhl}}(v) \to M^σ(v)$ from the Uhlenbeck compactification of $μ$-stable vector bundles.
Let $(X,H)$ be a smooth, projective, polarized surface over $\mathbb{C}$, and let $v \in K_{\mathrm{num}}(X)$ be a class of positive rank. We prove that for certain Bridgeland stability conditions $σ= (\mathcal{A}, Z)$ "on the vertical wall" for $v$, the good moduli space $M^σ(v)$ parameterizing S-equivalence classes of $σ$-semistable objects of class $v$ in $\mathcal{A}$ is projective. Moreover, we construct a bijective morphism $M^{\mathrm{Uhl}}(v) \to M^σ(v)$ from the Uhlenbeck compactification of $μ$-stable vector bundles.
