多边形与箭图的森理论及辛约化
Mori theory and symplectic reduction for polygons and quivers
AI总结：
该研究关联多边形与箭图模空间双有理几何中森理论与辛约化，分别在加法、乘法侧建立森模型与各类模空间的联系，匹配森腔分解与壁跨越，并计算小模型的代数自同构群。
AI中文摘要：
我们研究多边形与箭图模空间的双有理几何，重点关注森理论（Mori theory）与辛约化（symplectic reduction）之间的联系。在加法侧，我们将$Bl_{n-1}\boldsymbol{P}^{n-3}$的森模型与$\boldsymbol{P}^1$上点构型的GIT商、Hassett-GIT空间、带固定平凡丛的抛物商、箭图模空间及加法多边形空间相关联；在乘法侧，我们将$Bl_n\boldsymbol{P}^{n-3}$的森模型与平凡行列式的秩2抛物丛模空间、乘法多边形、乘法构型及紧乘法箭图商相关联。通过这种方式，森腔分解与对应加法、乘法辛约化的壁跨越匹配。最后，对这两种构造中出现的小模型，我们计算了对应的代数自同构群。
英文摘要：
We investigate the birational geometry of moduli spaces of polygons and quivers, emphasizing the link between Mori theory and symplectic reduction. On the additive side we relate Mori models of $Bl_{n-1}\mathbb{P}^{n-3}$ with GIT quotients of configurations of points on $\mathbb{P}^1$, Hassett--GIT spaces, parabolic quotients with fixed trivial bundle, quiver moduli spaces, and additive polygon spaces. On the multiplicative side we relate Mori models of $Bl_n\mathbb{P}^{n-3}$ with moduli spaces of rank two parabolic bundles with trivial determinant, multiplicative polygons, multiplicative configurations, and compact multiplicative quiver quotients. In this way, the Mori chamber decompositions are matched with wall-crossing for the corresponding additive and multiplicative symplectic quotients. Finally, for the small models appearing in these two constructions, we compute the corresponding groups of algebraic automorphisms.
