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タイトル: Uniformization of Cyclic Quotients of Multiplicative A-singularities
著者: Sasaki, Kenjiro
Takamura, Shigeru
キーワード: Uniformization of singularity
Monodromy
Degeneration of Riemann surfaces
Fractional Dehn twist
Small group
Pseudo-reflection group
発行日: 2016年6月24日
出版者: Graduate School of Mathematical Sciences, The University of Tokyo
掲載誌情報: Journal of Mathematical Sciences, The University of Tokyo. Vol. 23 (2016), No. 3, Page 675–726
抄録: This work is motivated by the canonical model of degenerations of Riemann surfaces. For a quotient space Ad−1/Γ of a 'multiplicative'A-singularity Ad−1 in Cn+1 under a certain cyclic group action Γ on Ad−1, we explicitly construct a small finite abelian subgroup G of GL(n, C) such that Ad−1/Γ ∼= Cn/G. A resolution of Cn/G gives a decomposition of the monodromy (a higher-dimensional fractional Dehn twist) of a degeneration Ad−1/Γ → C into subtwists along the exceptional set (it seems that T. Ashikaga’s work on resolutions is related to this). Moreover: (1) We give a numerical criterion for a certain subgroup of GL(n,C) to be small. (2) For a certain family of subgroups of GL(n, C), we show that if one subgroup of this family is small, then all subgroups of this family are small (equi-smallness theorem).
URI: http://hdl.handle.net/2261/72645
ISSN: 13405705
出現カテゴリ:Journal of Mathematical Sciences, the University of Tokyo
Journal of Mathematical Sciences, the University of Tokyo

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