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Algebraic Geometry Seminar
Seminar information archive ～09/19｜Next seminar｜Future seminars 09/20～
| Date, time & place | Friday 13:30 - 15:00 ハイブリッド開催/117Room #ハイブリッド開催/117 (Graduate School of Math. Sci. Bldg.) |
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| Organizer(s) | GONGYO Yoshinori, NAKAMURA Yusuke, TANAKA Hiromu |
2019/10/16
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Yusuke Sato (University of Tokyo/ IPMU)
Multidimensional continued fraction for Gorenstein cyclic quotient singularity
Yusuke Sato (University of Tokyo/ IPMU)
Multidimensional continued fraction for Gorenstein cyclic quotient singularity
[ Abstract ]
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.
