| Résume | This talk will describe some of my recent joint work with Tristan Ozuch.
Let (M, gi) be a non-collapsing sequence of smooth oriented compact Einstein 4-manifolds of fixed positive Einstein constant, and suppose that this sequence Gromov-Hausdorff converges to an Einstein orbifold that is Hermitian withrespect to some complex structure on the limit orbifold X. Also suppose that X has at least one singular point, and thatevery gravitational instanton that bubbles off from the given sequence is actually anti-self-dual. Then, for sufficiently large i, the given manifolds (M, gi) are all Kähler-Einstein. In particular, the limit orbifold X must be Kähler-Einstein and must moreover be one of the limit orbifolds classified by Odaka, Spotti, and Sun |
