If a smooth Fano manifold admits a Kähler-Ricci soliton, then for all sufficiently large k the canonical cone of X times complex projective k-space has a Calabi-Yau cone structure.
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From K\"ahler Ricci solitons to Calabi-Yau K\"ahler cones
If a smooth Fano manifold admits a Kähler-Ricci soliton, then for all sufficiently large k the canonical cone of X times complex projective k-space has a Calabi-Yau cone structure.