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Towards boundedness of minimal log discrepancies by the Riemann-Roch theorem
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 133, Number 5, October 2011
- pp. 1299-1311
- 10.1353/ajm.2011.0037
- Article
- Additional Information
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We introduce an approach via the Riemann-Roch theorem to the boundedness problem of minimal log discrepancies
in fixed dimension. After reducing it to the case of a Gorenstein terminal singularity, firstly we prove that
the minimal log discrepancy is bounded if either multiplicity or embedding dimension is bounded. Secondly we
recover the characterization of a Gorenstein terminal three-fold singularity by Reid, and the sharp bound for
its minimal log discrepancy by Markushevich, without explicit classification. Finally we provide the sharp
bound for a special four-fold singularity, whose general hyperplane section has a terminal piece.