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Shrinking gradient K\"ahler-Ricci solitons are simply-connected

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arxiv 2503.05838 v1 pith:STHTAYKN submitted 2025-03-06 math.DG math.AG

Carlos Esparza This is my paper · ORCID
classification math.DGmath.AG
keywords ahler-riccishrinkingsimply-connectedsolitonscoversfanofibrationsfinite
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Uniqueness of shrinking K\"ahler-Ricci solitons on resolutions of K\"ahler cones

    math.DG 2026-07 conditional novelty 7.0 of 10

    Every complete shrinking gradient Kähler-Ricci soliton on a resolution of a Kähler cone is asymptotically conical, which yields uniqueness up to pullback by biholomorphism.

  2. Compactness and Rigidity of Complete K\"ahler Ricci Shrinkers

    math.DG 2026-08 conditional novelty 6.0 of 10

    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.

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