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arXiv · 1310.6882

Singularities with respect to Mather-Jacobian discrepancies

Lawrence Ein·Shihoko Ishii
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Abstract

As is well known, the "usual discrepancy" is defined for a normal Q-Gorenstein variety. By using this discrepancy we can define a canonical singularity and a log canonical singularity. In the same way, by using a new notion, Mather-Jacobian discrepancy introduced in recent papers we can define a "canonical singularity" and a "log canonical singularity" for not necessarily normal or Q-Gorenstein varieties. In this paper, we show basic properties of these singularities, behavior of these singularities under deformations and determine all these singularities of dimension up to 2.

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Lawrence Ein, Shihoko Ishii. 2013-10-25. Singularities with respect to Mather-Jacobian discrepancies. https://arxiv.org/abs/1310.6882

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