On the Volume of Isolated Singularities
Algebraic Geometry
2019-02-20 v2
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 \Delta such that the pair (X,\Delta) is log canonical.
Keywords
Cite
@article{arxiv.1301.6121,
title = {On the Volume of Isolated Singularities},
author = {Yuchen Zhang},
journal= {arXiv preprint arXiv:1301.6121},
year = {2019}
}
Comments
12 pages. Final version. To appear in Compos. Math