An answer to a question raised by Shokurov on the minimal discrepancy of a terminal singularity of index 1 is given. It is proved that the minimal discrepancy is 1 (it is 2 for a non-singular point and 0 for all other canonical singularities of index 1). A rough classification of terminal singularities of index 1 based on finding certain low degree monomials in their equations, and the toric techniques of weighted blow ups are used. This result has been generalized to terminal singularities of index $r>1$ by Y.Kawamata; his theorem states that the minimal discrepancy is $1/r$.
雑誌名
Journal of mathematical sciences, the University of Tokyo
巻
3
号
2
ページ
445 - 456
発行年
1996
ISSN
13405705
書誌レコードID
AA11021653
フォーマット
application/pdf
日本十進分類法
415
Mathematical Reviews Number
MR1424437
Mathmatical Subject Classification
14E30(MSC1991)
14J30(MSC1991)
出版者
Graduate School of Mathematical Sciences, The University of Tokyo
原稿受領日
1995-11-07
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Minimal Discrepancy for a Terminal cDV Singularity Is 1
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