Towards boundedness of minimal log discrepancies by Riemann--Roch theorem

Details Towards boundedness of minimal log discrepancies by Riemann--Roch theorem Towards boundedness of minimal log discrepancies by Riemann--Roch theorem

2009-03-03

arxiv.org/abs/0903.0418v1

Mathematics

Algebraic Geometry

11 pages

Scientific paper

We introduce an approach of 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 its minimal log discrepancy is bounded if either multiplicity or embedding dimension is bounded. Secondly we recover the characterisation of a Gorenstein terminal three-fold singularity by Reid, and the precise boundary of its minimal log discrepancy by Markushevich, without explicit classification. Finally we provide the precise boundary for a special four-fold singularity, whose general hyperplane section has a terminal piece.

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