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arXiv · 2607.17878

$\Theta$-reductivity and $S$-completeness for adjoint Fano foliated structures

Theodoros Stylianos Papazachariou
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Abstract

We prove the valuative criteria of $\Theta$-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.

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Theodoros Stylianos Papazachariou. 2026-07-20. $\Theta$-reductivity and $S$-completeness for adjoint Fano foliated structures. https://arxiv.org/abs/2607.17878

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