TY - JOUR
T1 - On the proper moduli spaces of smoothable Kähler-Einstein Fano varieties
AU - Li, Chi
AU - Wang, Xiaowei
AU - Xu, Chenyang
N1 - Publisher Copyright:
© 2019, Duke University Press.
PY - 2019/6/1
Y1 - 2019/6/1
N2 - In this paper we investigate the geometry of the orbit space of the closure of the subscheme parameterizing smooth Kähler-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 Kähler-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.
AB - In this paper we investigate the geometry of the orbit space of the closure of the subscheme parameterizing smooth Kähler-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 Kähler-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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U2 - 10.1215/00127094-2018-0069
DO - 10.1215/00127094-2018-0069
M3 - Article
AN - SCOPUS:85067118479
SN - 0012-7094
VL - 168
SP - 1387
EP - 1459
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 8
ER -