论文标题
立方四倍的K稳定性
K-stability of cubic fourfolds
论文作者
论文摘要
我们证明了立方四倍的K-Moduli空间与它们的GIT模量空间相同。更确切地说，立方四倍的K-（半/多）稳定性与相应的GIT稳定性一致，Laza详细研究了相应的GIT稳定性。特别是，这意味着所有光滑的立方四倍均承认Kähler-Einstein指标。关键成分是由于Liu-XU引起的局部体积估计值，以及Ambro-Kawamata对Fano Fourdolds的非呈现定理。
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-Xu, and Ambro-Kawamata's non-vanishing theorem for Fano fourfolds.
