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.References
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Bibliographic Information
- Tsung-Ju Lee
- Affiliation: Center of Mathematical Sciences and Applications, Harvard University, 20 Garden Street, Cambridge, Massachusetts 02138
- MR Author ID: 1278815
- ORCID: 0000-0002-0865-0564
- Email: tjlee@cmsa.fas.harvard.edu
- Yu-Shen Lin
- Affiliation: Department of Mathematics, Boston University, 111 Cummington Mall, Boston, Massachusetts 02215
- MR Author ID: 1192962
- ORCID: 0000-0002-8496-6026
- Email: yslin@bu.edu
- Received by editor(s): September 9, 2022
- Received by editor(s) in revised form: November 4, 2022
- Published electronically: May 17, 2023
- Additional Notes: The first author was supported by the Simons Collaboration on HMS Grant and the AMS–Simons Travel Grant (2020–2023). The second author was supported by Simons collaboration grant # 635846 and NSF grant DMS #2204109.
- © Copyright 2023 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 376 (2023), 5461-5501
- MSC (2020): Primary 53C26
- DOI: https://doi.org/10.1090/tran/8856
- MathSciNet review: 4630751