Seminars
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
Calendar
Search
Add a seminar

RSS
Forthcoming seminars




Shafarevich Seminar
September 7, 2021 15:00, Moscow, Steklov Mathematical Institute, Room. 104 (8 Gubkina) + Zoom
 


Gromov-Hausdorff limits of hyperkahler metrics

M. S. Verbitsky
Video records:
MP4 3,811.0 Mb

Number of views:
This page:462
Video files:194



Abstract: Gromov defined a structure of a metric space on the set of isometry classes of metric spaces, and applied its convergence properties in areas as diverse as symplectic geometry and group theory. This metric is often called "Gromov-Hausdorff metric". I would explain what happens with Gromov-Hausdorff convergence in hyperkahler geometry.
Let $(M,I)$ be a holomorphically symplectic compact Kahler manifold, and $W$ the space of all hyperkahler metrics on all birational models of $(M,I)$. I will show that the set of Gromov-Hausdorff limits of points in $W$ contains all hyperkahler metrics on $M$. This is surprising, because the dimension of $W$ is $b_2-2$, and the dimension of its closure is at least $3b_2-8$: typically, much bigger.

Language: English
 
  Contact us:
 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024