AI 中文总结
研究伴随Fano叶状结构模问题，通过发展混合Ding理论等方法，证明了Θ-约化性和S-完备性的赋值准则，给出族的相对扩张定理，并应用于证明t-K-多稳定退化唯一性等结论。
AI 中文摘要
我们证明了t-K-半稳定伴随Fano叶状结构模问题的Θ-约化性和S-完备性的赋值准则。我们为任意线性有界乘法滤层发展了混合Ding理论，证明了伴随叶状结构与任意理想的伴随逆定理，并建立了相对提取和有限生成定理。这些结果共同给出了所需的族的相对扩张定理。作为应用，我们证明了t-K-多稳定退化的唯一性、t-K-多稳定伴随Fano叶状结构自同构群的约化性以及t-K-稳定情形下自同构群的有限性。
英文摘要
We prove the valuative criteria of $Θ$-reductivity and $S$-completeness for the moduli problem of $t$-K-semistable adjoint Fano foliated structures. We develop a mixed Ding theory for arbitrary linearly bounded multiplicative filtrations, prove inversion of adjunction with arbitrary ideals for adjoint foliated structures, and establish a relative extraction and finite generation theorem. Together, these results yield the required relative extension theorems for families. As applications, we prove uniqueness of $t$-K-polystable degenerations, reductivity of the automorphism group of $t$-K-polystable adjoint Fano foliated structures, and finiteness of the automorphism group in the $t$-K-stable case.
Comments46 pages. Comments very welcome!
