A new first-order visibility argument derives compactness, splitting, and Gaussian rigidity for complete Kähler-Ricci shrinkers from the weight structure of their polarized Fano fibrations.
Shrinking gradient K\"ahler-Ricci solitons are simply-connected
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abstract
We show that smooth polarized Fano fibrations have no nontrivial finite covers. Using results by Sun-Zhang and Wylie, it follows that shrinking K\"ahler-Ricci solitons are simply-connected.
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math.DG 1years
2026 1verdicts
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Compactness and Rigidity of Complete K\"ahler Ricci Shrinkers
A new first-order visibility argument derives compactness, splitting, and Gaussian rigidity for complete Kähler-Ricci shrinkers from the weight structure of their polarized Fano fibrations.