PERIOD DOMAINS FOR GRAVITATIONAL INSTANTONS

Tsung Ju Lee; Yu Shen Lin

doi:10.1090/tran/8856

PERIOD DOMAINS FOR GRAVITATIONAL INSTANTONS

Tsung Ju Lee, Yu Shen Lin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 ALH^∗, ALG, and ALG^∗ gravitational instantons are surjective. In particular, the period domains of these gravitational instantons are exactly their moduli spaces.

Original language	English
Pages (from-to)	5461-5501
Number of pages	41
Journal	Transactions of the American Mathematical Society
Volume	376
Issue number	8
DOIs	https://doi.org/10.1090/tran/8856
Publication status	Published - 2023

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/tran/8856

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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 ALH∗, ALG, and ALG∗ gravitational instantons are surjective. In particular, the period domains of these gravitational instantons are exactly their moduli spaces.",

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AB - 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 ALH∗, ALG, and ALG∗ gravitational instantons are surjective. In particular, the period domains of these gravitational instantons are exactly their moduli spaces.

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PERIOD DOMAINS FOR GRAVITATIONAL INSTANTONS

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