Period domains for gravitational instantons

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 A L H ∗ \mathrm {ALH}^{\ast } , A L G \mathrm {ALG} , and A L G ∗ \mathrm {ALG}^{\ast } gravitational instantons are surjective. In particular, the period domains of these gravitational instantons are exactly their moduli spaces.