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代数幾何学セミナー
過去の記録 ～04/18｜次回の予定｜今後の予定 04/19～
| 開催情報 | 金曜日 13:30～15:00 数理科学研究科棟(駒場) ハイブリッド開催/117号室 |
|---|---|
| 担当者 | 權業 善範、中村 勇哉、田中 公 |
2019年10月16日(水)
15:30-17:00 数理科学研究科棟(駒場) 122号室
佐藤 悠介 氏 (東大数理/ IPMU)
Multidimensional continued fraction for Gorenstein cyclic quotient singularity
佐藤 悠介 氏 (東大数理/ IPMU)
Multidimensional continued fraction for Gorenstein cyclic quotient singularity
[ 講演概要 ]
Let G be a finite cyclic subgroup of GL(n,C). Then Cn/G is a cyclic quotient singularity. In the case n = 2, Cn/G possess the unique minimal resolution, and it is obtained by Hirzubruch-Jung continued fraction. In this talk, we show a sufficient condition of existence of crepant desingularization for Gorenstein abelian quotient singularities in all dimensions by using Ashikaga’s continuous fractions. Moreover, as a corollary, we prove that all three dimensional Gorenstein abelian quotient singularities possess a crepant desingularization.
Let G be a finite cyclic subgroup of GL(n,C). Then Cn/G is a cyclic quotient singularity. In the case n = 2, Cn/G possess the unique minimal resolution, and it is obtained by Hirzubruch-Jung continued fraction. In this talk, we show a sufficient condition of existence of crepant desingularization for Gorenstein abelian quotient singularities in all dimensions by using Ashikaga’s continuous fractions. Moreover, as a corollary, we prove that all three dimensional Gorenstein abelian quotient singularities possess a crepant desingularization.
