论文标题
两极化品种的估值稳定性
Valuative stability of polarised varieties
论文作者
论文摘要
藤田和李在与估值相关的数量方面赋予了Fano品种的K稳定性的特征，这对于该地区的所有最新进展至关重要。我们引入了对任意两极化品种的评估稳定性的概念，并表明它等于K稳定性相对于具有整体中心纤维的测试配置。基于估算稳定性的数值不变稳定性是基于富士的beta不变式建模的，但包括涉及体积导数的术语。我们提供了几个有价值稳定和不稳定品种的例子，包括复我们还讨论了三角洲不变性在对偏光品种的估算稳定性和K稳定性的研究中所扮演的作用。
Fujita and Li have given a characterisation of K-stability of a Fano variety in terms of quantities associated to valuations, which has been essential to all recent progress in the area. We introduce a notion of valuative stability for arbitrary polarised varieties, and show that it is equivalent to K-stability with respect to test configurations with integral central fibre. The numerical invariant governing valuative stability is modelled on Fujita's beta invariant, but includes a term involving the derivative of the volume. We give several examples of valuatively stable and unstable varieties, including the toric case. We also discuss the role that the delta invariant plays in the study of valuative stability and K-stability of polarised varieties.
