SNC K\"ahler-Einstein metrics and RCD spaces

Martin de Borbon; Cristiano Spotti

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arXiv · 2601.18741

SNC K\"ahler-Einstein metrics and RCD spaces

Martin de Borbon·Cristiano Spotti

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Abstract

We show that K\"ahler-Einstein metrics with cone singularities along simple normal crossing (SNC) divisors define RCD spaces, both in the compact setting and in certain non-compact cases, thereby producing many examples of Einstein RCD spaces. In particular, we show the existence of smooth non-compact $4$-manifolds carrying ALE Ricci-flat RCD$(0,4)$ metrics with any space form $S^3/\Gamma$ as the link of the tangent cone at infinity, answering a question raised by D. Semola. Our proofs rely on the characterization of RCD spaces in the almost-smooth setting due to S. Honda and Honda-Sun.

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Martin de Borbon, Cristiano Spotti. 2026-01-26. SNC K\"ahler-Einstein metrics and RCD spaces. https://arxiv.org/abs/2601.18741

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