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arXiv · 1301.6121

On the Volume of Isolated Singularities

Yuchen Zhang
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Abstract

We give an equivalent definition of the local volume of an isolated singularity Vol_{BdFF}(X,0) given in [BdFF12] in the Q-Gorenstein case and we generalize it to the non-Q-Gorenstein case. We prove that there is a positive lower bound depending only on the dimension for the non-zero local volume of an isolated singularity if X is Gorenstein. We also give a non-Q-Gorenstein example with Vol_{BdFF}(X,0)=0, which does not allow a boundary Δsuch that the pair (X,Δ) is log canonical.

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Yuchen Zhang. 2013-11-12. On the Volume of Isolated Singularities. https://doi.org/10.1112/s0010437x13007847

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