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arXiv · 2502.11847

Minimal log discrepancy and orbifold curves

Chi Li·Zhengyi Zhou
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Abstract

We show that the minimal log discrepancy of any isolated Fano cone singularity is at most the dimension of the variety. This is based on its relation with dimensions of moduli spaces of orbifold rational curves. We also propose a conjectural characterization of weighted projective spaces as Fano orbifolds in terms of orbifold rational curves, which would imply the equality holds only for smooth points.

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Chi Li, Zhengyi Zhou. 2025-02-17. Minimal log discrepancy and orbifold curves. https://arxiv.org/abs/2502.11847

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