  For any manifold $N^p$ admitting an Einstein metric with positive Einstein
constant, we study the behavior of the Ricci flow on high-dimensional products
$M = N^p \times S^{q+1}$ with doubly-warped product metrics. In particular, we
provide a rigorous construction of local, type II, conical singularity
formation on such spaces. It is shown that for any $k > 1$ there exists a
solution with curvature blow-up rate $\| Rm \|_{\infty} (t) \gtrsim (T-t)^{-k}$
with singularity modeled on a Ricci-flat cone at parabolic scales.

Differential Geometry