Relative Ding and K-stability of toric Fano manifolds in low dimensions
Relative Ding and K-stability of toric Fano manifolds in low dimensions
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DOI：
10.1007/s40879-023-00617-0
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发表时间：
2023-04
影响因子：
0.6
通讯作者：
Yasufumi Nitta;Shunsuke Saito;N. Yotsutani
中科院分区：
文献类型：
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作者：
Yasufumi Nitta;Shunsuke Saito;N. Yotsutani
本文的目的是澄清所有的一致相对稳定的复曲面Fano三重和四重以及不稳定的。在我们的分类结果中，关键的参与者是马渊常数，由于Yao的工作，它可以通过相关矩多面体的组合数据来计算（Int Math Res Not IMRN 2022（24）：19790-19853，2022）。本文利用Mabuchi常数的值给出了四维以下复曲面Fano流形的一致相对Ding稳定性的列表。作为主要定理的应用，我们通过考虑某些特殊的环面Fano流形，阐明了相对K-稳定性与相对Ding稳定性的区别。在证明中，我们使用了相对不稳定的环面Fano流形的Bott塔结构。
The purpose of this article is to clarify all of the uniformly relatively Ding stable toric Fano threefolds and fourfolds as well as unstable ones. The key player in our classification result is the Mabuchi constants, which can be calculated by combinatorial data of the associated moment polytopes due to the work of Yao (Int Math Res Not IMRN 2022(24):19790–19853, 2022). In this article, we give the list of uniform relative Ding stability of all toric Fano manifolds in dimension up to four with the values of the Mabuchi constants. As an application of our main theorem, we clarify the difference between relativeK-stability and relative Ding stability by considering some specific toric Fano manifolds. In the proof, we used Bott tower structure of relatively Ding unstable toric Fano manifolds.