期刊
DUKE MATHEMATICAL JOURNAL
卷 168, 期 8, 页码 1387-1459出版社
DUKE UNIV PRESS
DOI: 10.1215/00127094-2018-0069
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资金
- National Science Foundation (NSF) [DMS-1405936]
- Simons Foundation Collaboration Grant for Mathematicians [281299]
- NSF [DMS-1609335, DMS-1128155, DMS-1252158]
- Recruitment Program of Foreign Experts grant
- Ky Fan and Yu-Fen Fan Membership Funds
- S. S. Chern Foundation
In this paper we investigate the geometry of the orbit space of the closure of the subscheme parameterizing smooth Kohler-Einstein Fano manifolds inside an appropriate Hilbert scheme. In particular, we prove that being K-semistable is a Zariski-open condition, and we establish the uniqueness of the Gromov-Hausdorff limit for a punctured flat family of Kohler-Einstein Fano manifolds. Based on these, we construct a proper scheme parameterizing the S-equivalent classes of Q-Gorenstein smoothable, K-semistable Q-Fano varieties, and we verify various necessary properties to guarantee that it is a good moduli space.
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