In the last talk we had seen the definition of Gromov-Hausdorff metric and its convergence and some examples.
In particular, we had discussed in the example of Hopf fibration by taking quotients in $\Bbb S^3\to \Bbb S^2$ how the fiber actually collapses along the Gromov-Hausdorff convergence.
In today's talk we will discuss a example in that the Kahler-Ricci flow on the manifold
$$X_{m,n}=\Bbb P\left(\mathcal O_{\Bbb P^n} \oplus\mathcal O_{\Bbb P^n}(-1)^{\oplus(m+1)}\right)$$
converges to $\Bbb P^n$ with constant multiople of the Fubini-Study metric for some particular case and to a point in some other case.
The talk is based on fourth chapter on the paper
Metric Flips with Calabi Ansatz by Jian Song and Yuan Yuan.