AI 中文总结
本文针对来自四元数向量空间$\boldsymbol{\rm H}^n$的超双曲商空间，在假设Kirwan映射满射下证明周期映射双射的托雷利型定理，将Kronheimer的ALE引力瞬子托雷利型定理推广至代数几何领域，适用于toric超双曲簇与Nakajima quiver簇。
AI 中文摘要
本文研究来自四元数向量空间$\boldsymbol{\rm H}^n$的超双曲商空间上代数渐近超双曲结构的模空间，考虑该模空间上的周期映射，并在假设Kirwan映射满射的条件下证明了托雷利型定理（即周期映射的双射性）。该工作为Kronheimer（1989）关于ALE引力瞬子的托雷利型定理提供了代数几何推广，特别地，该定理适用于 toric 超双曲簇与Nakajima quiver簇。
英文摘要
In this paper, we investigate the moduli space of algebraic asymptotic hyperkähler structures on hyperkähler quotients arising from a quaternionic vector space $\mathbb{H}^n$. We consider the period map on this moduli space, and prove a Torelli-type theorem (i.e., the bijectivity of the period map) assuming the surjectivity of the Kirwan map. This work provides an algebro-geometric generalization of the Torelli-type theorem for ALE gravitational instantons by Kronheimer (1989). In particular, this theorem applies to toric hyperkähler varieties and Nakajima quiver varieties.
Comments28 pages
