AI 中文总结
该研究针对满足J-大性和特定边界锥条件的紧致凯勒流形，证明了J-零轨迹与J-非丰富轨迹等价，核心工具为广义Khovanskii-Teissier不等式。
AI 中文摘要
对于具有一对凯勒类(α,β)的n维紧致凯勒流形X，我们证明在J-大性（对于至多3维的半稳定对自动成立，见文献[3d]）及存在凯勒形式ω∈α、χ∈β满足边界锥条件c_{α,β}ω^{n-1}-(n-1)ω^{n-2}∧χ≥0的假设下，代数定义的J-零轨迹等于解析定义的J-非丰富轨迹。关键工具是Collins在文献[CT21]中提出的与J方程相关的广义Khovanskii-Teissier不等式及其对奇异凯勒空间的推广。
英文摘要
For a $n$-dimensional compact Kähler manifold $X$ with a pair of Kähler classes $(α,β)$, we show that the algebraically defined $J$-null locus is equal to the analytically defined $J$-non-ample locus under the assumption of $J$-bigness(which is automatic for semistable pair up to dimension $3$ \cite{3d}), and boundary cone condition $c_{α,β}ω^{n-1}-(n-1)ω^{n-2}\wedgeχ\geq 0$ for some Kähler form $ω\in α,χ\in β$. The key tool is the generalized Khovanskii-Teissier inequality associated to $J$ equation formulated by Collins \cite{CT21} and its extension to singular Kähler space.
