Year: 2026
Type: preprint
Abstract: 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) under mild assumptions including 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.
Source: arXiv (Cornell University)
Author: Kotani, Ryota
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7202195960