Seminar on Geometric Complex Analysis

Seminar information archive ~06/24Next seminarFuture seminars 06/25~

Date, time & place Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.)
Organizer(s) Kengo Hirachi, Shigeharu Takayama

2017/05/15

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Kota Hattori (Keio University)
On the moduli spaces of the tangent cones at infinity of some hyper-Kähler manifolds
[ Abstract ]
For a metric space $(X,d)$, the Gromov-Hausdorff limit of $(X, a_n d)$ as $a_n \rightarrow 0$ is called the tangent cone at infinity of $(X,d)$. Although the tangent cone at infinity always exists if $(X,d)$ comes from a complete Riemannian metric with nonnegative Ricci curvature, the uniqueness does not hold in general. Colding and Minicozzi showed the uniqueness under the assumption that $(X,d)$ is a Ricci-flat manifold satisfying some additional conditions.
In this talk, I will explain a example of noncompact complete hyper-Kähler manifold who has several tangent cones at infinity, and determine the moduli space of them.