An effective construction of asymptotically conical Calabi--Yau manifolds with irregular Reeb vectors

par Trung Nghiem (Institut Camille Jordan)

jeudi 5 févr. 2026, 10:30 → 11:30 Europe/Paris

An asymptotically conical Calabi--Yau manifold is a Ricci-flat Kähler manifold whose shape, when zoomed out towards infinity, looks like a Calabi--Yau cone. A recent work of Conlon--Hein shows that an AC Calabi--Yau manifold is obtained either by algebraic deformations or crepant resolution in a reversible and exhaustive process. In terms of the metric on the cone, the behavior of the AC Calabi--Yau metric is said to be quasi-regular or irregular. Examples of the latter are notoriously rare in the literature. In my talk, I'll present an effective strategy to construct irregular AC Calabi--Yau manifolds via Altmann's deformation theory of toric Calabi--Yau cones. This is a joint work with Ronan J. Conlon (University of Texas, Dallas).