A higher-dimensional Kummer construction associates K3^[3]-type hyper-Kähler sixfolds to Kum^3-type sixfolds, with applications to motives, derived categories, and algebraic cycle conjectures.
Stability conditions on Kuznetsov components
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abstract
We introduce a general method to induce Bridgeland stability conditions on semiorthogonal components of triangulated categories. In particular, we prove the existence of Bridgeland stability conditions on the Kuznetsov component of the derived category of Fano threefolds and of cubic fourfolds. As an application, in the appendix, written jointly with Xiaolei Zhao, we give a variant of the proof of the Torelli theorem for cubic fourfolds by Huybrechts and Rennemo.
years
2026 2representative citing papers
Any Farey triangle corresponds to a variant of the Colmez-Fontaine fundamental lemma, with the original lemma matching the triangle (1/0, 1/1, 0/1).
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The hyper-Kummer construction
A higher-dimensional Kummer construction associates K3^[3]-type hyper-Kähler sixfolds to Kum^3-type sixfolds, with applications to motives, derived categories, and algebraic cycle conjectures.
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Modular variants of p-adic fundamental sequence
Any Farey triangle corresponds to a variant of the Colmez-Fontaine fundamental lemma, with the original lemma matching the triangle (1/0, 1/1, 0/1).