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arXiv · 2508.21676

Local inequalities for $cA_k$ singularities

Igor Krylov·Takuzo Okada·Erik Paemurru
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Abstract

We generalize an intersection-theoretic local inequality of Fulton-Lazarsfeld to weighted blowups. As a consequence, we obtain the $4n^2/(k+1)$-inequality for isolated $cA_k$ singularities, an analogue of the $4 n^2$-inequality for smooth points. We use this to prove birational rigidity of many families of Fano 3-fold weighted complete intersections with terminal quotient singularities and isolated $cA_k$ singularities, including sextic double solids with $cA_1$ and ordinary $cA_2$ points.

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Igor Krylov, Takuzo Okada, Erik Paemurru. 2025-08-29. Local inequalities for $cA_k$ singularities. https://arxiv.org/abs/2508.21676

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