Conical Calabi-Yau metrics on toric cones

Thời gian: 14:00 đến 15:30 Ngày 16/08/2022

Địa điểm: C102, VIASM

Báo cáo viên: Nghiêm Trần Trung

Tóm tắt:

We give the definition and structure of cones with an isolated singularity, often called "smooth cones". A smooth cone is also a normal affine variety. A Kähler cone contains a Riemannian manifold of odd dimension, on which there exists a transverse Kähler structure.  Finding the Calabi-Yau metrics on smooth cones is equivalent to solving a Kähler-Einstein-type complex Monge-Ampère equation on the transverse Kähler structure. This generalizes the uniformization problem from compact complex manifolds to normal affine varieties. In the toric case, the existence of Calabi-Yau metrics on the cone is equivalent to a volume minimization principle on the defining cone of the toric variety. This principle is also true in the singular case.