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arXiv · 2608.08680

A Torelli-type theorem for hyperk\"{a}hler quotients

Ryota Kotani
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Abstract

In this paper, we investigate the moduli space of algebraic asymptotic hyperk\"ahler structures on hyperk\"ahler 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 hyperk\"ahler varieties and Nakajima quiver varieties.

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Ryota Kotani. 2026-08-09. A Torelli-type theorem for hyperk\"{a}hler quotients. https://arxiv.org/abs/2608.08680

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