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A Torelli-type theorem for hyperkähler quotients
Abstract
In this paper, we investigate the moduli space of algebraic asymptotic hyperkähler structures on hyperkähler quotients arising from a quaternionic vector space ℍn. 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.
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BibTeX
@misc{kotani2026torellitype,
title = {{A Torelli-type theorem for hyperkähler quotients}},
author = {Ryota Kotani},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2608.08680},
eprint = {2608.08680},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.08680},
}
RIS
TY - UNPB
TI - A Torelli-type theorem for hyperkähler quotients
AU - Ryota Kotani
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2608.08680
UR - https://arxiv.org/abs/2608.08680
AB - In this paper, we investigate the moduli space of algebraic asymptotic hyperkähler structures on hyperkähler quotients arising from a quaternionic vector space 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.
ER -