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arXiv · 1903.07202

Bounded deformations of $(\epsilon,\delta)$-log canonical singularities

Jingjun Han·Jihao Liu·Joaquín Moraga
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Abstract

In this paper we study $(\epsilon,\delta)$-lc singularites, i.e. $\epsilon$-lc singularities admitting a $\delta$-plt blow-up. We prove that $n$-dimensional $(\epsilon,\delta)$-lc singularities are bounded up to a deformation, and $2$-dimensional $(\epsilon,\delta)$-lc singularities form a bounded family. Furthermore, we give an example which shows that $(\epsilon,\delta)$-lc singularities are not bounded in higher dimensions, even in the analytic sense.

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Jingjun Han, Jihao Liu, Joaquín Moraga. 2019-03-17. Bounded deformations of $(\epsilon,\delta)$-log canonical singularities. https://arxiv.org/abs/1903.07202

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