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.
Gromov-Hausdorff convergence, Calabi ansatz, Kähler-Ricci flow
The talk is based on fourth chapter on the paper Metric Flips with Calabi Ansatz by Jian Song and Yuan Yuan.
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