# Singularities with the highest Mather minimal log discrepancy

@article{Ishii2013SingularitiesWT,
title={Singularities with the highest Mather minimal log discrepancy},
author={Shihoko Ishii and Ana J. Reguera},
journal={Mathematische Zeitschrift},
year={2013},
volume={275},
pages={1255-1274}
}
• Published 25 April 2013
• Mathematics
• Mathematische Zeitschrift
This paper characterizes singularities with Mather minimal log discrepancies in the highest unit interval, i.e., the interval between $$d-1$$d−1 and $$d$$d, where $$d$$d is the dimension of the scheme. The class of these singularities coincides with one of the classes of (1) compound Du Val singularities, (2) normal crossing double singularities, (3) pinch points, and (4) pairs of non-singular varieties and boundaries with multiplicities less than or equal to 1 at the point. As a corollary, we…
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