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.
K\"ahler-Ricci Tangent Flows are Infinitesimally Algebraic
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abstract
We show that any tangent cone of a singular shrinking K\"ahler-Ricci soliton is a normal affine algebraic variety. Moreover, the regular set of such a tangent cone in the metric sense coincides with the regular set in the algebraic sense. Along the way, we give a parabolic proof of H\"ormander's $L^{2}$ estimate, which can be used to solve the $\overline{\partial}$-equation on any singular shrinking K\"ahler-Ricci soliton.
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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.