Singularity criteria for K-stability of adjoint foliated structures
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917538654322688 |
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| author | Papazachariou, Theodoros Stylianos |
| author_facet | Papazachariou, Theodoros Stylianos |
| contents | We prove singularity criteria for the $t$-K-stability of adjoint foliated structures. We first show that K-semistability of adjoint foliated structures implies log canonicity by extending Odaka's flag ideal characterisation of the mixed Donaldson--Futaki invariant to the adjoint foliated setting. We then prove that adjoint Calabi--Yau foliated structures are K-semistable, and klt ones are K-stable, while log canonical adjoint general type foliated structures are K-stable with respect to the canonical polarisation. We also show that K-semistable adjoint Fano foliated structures are klt. In particular, their ambient varieties are potentially klt and of Fano type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28140 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Singularity criteria for K-stability of adjoint foliated structures Papazachariou, Theodoros Stylianos Algebraic Geometry We prove singularity criteria for the $t$-K-stability of adjoint foliated structures. We first show that K-semistability of adjoint foliated structures implies log canonicity by extending Odaka's flag ideal characterisation of the mixed Donaldson--Futaki invariant to the adjoint foliated setting. We then prove that adjoint Calabi--Yau foliated structures are K-semistable, and klt ones are K-stable, while log canonical adjoint general type foliated structures are K-stable with respect to the canonical polarisation. We also show that K-semistable adjoint Fano foliated structures are klt. In particular, their ambient varieties are potentially klt and of Fano type. |
| title | Singularity criteria for K-stability of adjoint foliated structures |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2605.28140 |