Period domains for gravitational instantons

Lee, Tsung-Ju; Lin, Yu-Shen

doi:10.1090/tran/8856

Period domains for gravitational instantons
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by Tsung-Ju Lee and Yu-Shen Lin

Trans. Amer. Math. Soc. 376 (2023), 5461-5501

DOI: https://doi.org/10.1090/tran/8856

Published electronically: May 17, 2023

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Abstract:

Based on the uniformization theorems of gravitation instantons by Chen–Chen [Acta Math. 227 (2021), pp. 263–307], Chen–Viaclovsky [Gravitational instantons with quadratic volume growth, 2021], Collins–Jacob–Lin [Forum Math. Sigma (2021)], and Hein–Sun–Viaclovsky–Zhang [Gravitational instantons and del Pezzo surfaces], we prove that the period maps for the $\mathrm {ALH}^{\ast }$, $\mathrm {ALG}$, and $\mathrm {ALG}^{\ast }$ gravitational instantons are surjective. In particular, the period domains of these gravitational instantons are exactly their moduli spaces.

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