中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
代数几何研讨班
Speaker: Theodoros Papazachariou（清华大学）
Inviter: 欧文浩
Language: English
Title: K-stability for adjoint foliated structures
Time & Venue: 2026年9月8日（星期二） 14:00-15:00 思源楼S818
Abstract: In recent years, K-stability has played a central role in the construction of moduli spaces of Fano varieties and log Fano pairs, building on major advances in birational geometry. In parallel, substantial progress has been made on the birational geometry and minimal model programme for adjoint foliated structures, namely varieties equipped with an algebraically integrable foliation and suitable adjoint data. This raises the question of whether K-stability can be extended to this setting and used to develop a corresponding moduli theory. In this talk, I will introduce a notion of K-stability for adjoint foliated structures via test configurations and explain the resulting singularity criteria. I will then discuss how the adjoint foliated MMP allows us, in the Fano setting, to reduce the study of K-stability to special test configurations. This leads to birational invariants analogous to those appearing in the usual theory of K-stability. Finally, I will explain how these invariants can be used to prove boundedness of the K-semistable locus and, show how uniqueness of K-polystable degenerations and reductivity of K-polystable automorphism groups follows. These results provide key ingredients towards a moduli theory of adjoint Fano foliated structures.
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