Singular limits of Kähler-Ricci flow on Fano \(G\)-manifolds (Q6652941)

A Fano manifold \(M\) is a compact Kähler manifold with positive first Chern class \(c_1(M)\). Ricci flow (introduced by Hamilton in the early 1980s) preserves the Kähler structure. The Kähler-Ricci flow is the Ricci flow restricted to Kähler metrics. For \(M\) a Fano compactification of a semisimple complex Lie group \(G\) and \(\omega_0\) a \(K\times K\)-invariant metric in \(2\pi c_1(M)\), where \(K\) is a maximal compact subgroup of \(G\), the authors prove that the solution of the Kähler-Ricci flow with \(\omega_0\) as an initial metric on \(M\), is of type II, if \(M\) admits no Kähler-Einstein metrics. As an application, they find two Fano compactifications of \(SO_4(\mathbb{C})\) and one Fano compactification of \(Sp_4(\mathbb{C})\), on which the Kähler-Ricci flow will develop singularities of type II. These might be the first examples of Ricci flow with singularities of type II on Fano manifolds in the literature.