TY - JOUR
T1 - K-stability of cubic fourfolds
AU - Liu, Yuchen
N1 - Publisher Copyright:
© 2022 Walter de Gruyter GmbH, Berlin/Boston.
PY - 2022/5/1
Y1 - 2022/5/1
N2 - We prove that the K-moduli space of cubic fourfolds is identical to their GIT moduli space. More precisely, the K-(semi/poly)stability of cubic fourfolds coincide to the corresponding GIT stabilities, which was studied in detail by Laza. In particular, this implies that all smooth cubic fourfolds admit Kähler-Einstein metrics. Key ingredients are local volume estimates in dimension three due to Liu and Xu, and Ambro-Kawamata's non-vanishing theorem for Fano fourfolds.
AB - We prove that the K-moduli space of cubic fourfolds is identical to their GIT moduli space. More precisely, the K-(semi/poly)stability of cubic fourfolds coincide to the corresponding GIT stabilities, which was studied in detail by Laza. In particular, this implies that all smooth cubic fourfolds admit Kähler-Einstein metrics. Key ingredients are local volume estimates in dimension three due to Liu and Xu, and Ambro-Kawamata's non-vanishing theorem for Fano fourfolds.
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U2 - 10.1515/crelle-2022-0002
DO - 10.1515/crelle-2022-0002
M3 - Article
AN - SCOPUS:85125932705
SN - 0075-4102
VL - 2022
SP - 55
EP - 77
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 786
ER -