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arXiv · 2508.19893

Lech-Mumford constant and stability of local rings

Linquan Ma·Ilya Smirnov
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Abstract

We study further Mumford's notion of local semistability and, in particular, show that semistable singularities are log canonical under mild assumptions. We provide many new examples of semistable and unstable singularities. More generally, we develop the theory of the Lech-Mumford constant, an invariant defined as an optimal constant in the Lech inequality.

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Linquan Ma, Ilya Smirnov. 2025-08-27. Lech-Mumford constant and stability of local rings. https://arxiv.org/abs/2508.19893

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