Smoothness of the Universal Deformation Space of Compact Calabi-Yau Manifolds and Its Peterson-Weil Metric
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Kovalev has sketched a general deformation theory for asymptotically cylindrical Calabi-Yau manifolds, but his parameter count is not entirely accurate and he needs to assume an appropriate analog of the Tian-Todorov theorem, which seems still unknown.
“Indeed, Kovalev [35] has sketched a general deformation theory for asymptotically cylindrical Calabi-Yau manifolds, similar to Koiso's approach [33] in the compact case.However, his parameter count is not entirely accurate, and he needs to assume an appropriate analog of the Tian-Todorov theorem [51,55], which seems to be still unknown; cf.Corollary 4.3.”
From Gravitational instantons from rational elliptic surfaces (2011) · cites this paper as [51]
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Gravitational instantons from rational elliptic surfaces
Hein, H.-J. (2011) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-2011-00723-6 · Cited by 87 · see citing works
- Authors
- Tian, G.
- Affiliations
- University of California San Diego (US)
- Corresponding author
- Tian, Gang
- ORCID
- Tian, Gang
- Venue
- Mathematical Aspects of String Theory
- Publisher
- WORLD SCIENTIFIC
- Published
- 1987-09
- Pages
- 629-646
- OpenAlex
- W2025291128
- Cited by
- 305
- References
- 0
- Citations by year
- 2026: 3 · 2025: 11 · 2024: 9 · 2023: 4 · 2022: 10 · 2021: 19 · 2020: 15 · 2019: 13 · 2018: 18 · 2017: 6 · 2016: 9 · 2015: 8 · 2014: 10 · 2013: 9 · 2012: 5
- FWCI
- 5.68
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- Mathematical Aspects of String Theory (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Geometry and complex manifolds
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic Geometry and Number Theory
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Keywords
- smoothness, deformation theory
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