2026/07/20 by Theodoros Stylianos Papazachariou
#math.AG
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.