K-stability of cubic fourfolds
K-stability of cubic fourfolds
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DOI：
10.1515/crelle-2022-0002
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发表时间：
2020-07
期刊：
影响因子：
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通讯作者：
Yuchen Liu
中科院分区：
文献类型：
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作者：
Yuchen Liu
本文证明了三次四重模的K-模空间与它们的GIT模空间是一致的。更准确地说，三次四重的K-（半/多）稳定性与相应的GIT稳定性相一致，这是由Laza详细研究的。特别是，这意味着所有光滑三次四重都承认凯勒-爱因斯坦度量。关键成分是局部体积估计三维由于刘和徐，和安布罗河-川俣的非零定理Fano四倍。
Abstract 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.