Pencil genus for normal surface singularities

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概要

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• Let (X,o) be a normal complex surface singularity. We define an invariant pe(X,o) for (X,o) in terms of pencils of compact complex curves. Similarly, for a pair of (X,o) and h∈$¥mathfrak m$X,o (the maximal ideal of $¥mathscr{O}$X,o), we define an invariant pe(X,o,h). We call pe(X,o) (resp. pe(X,o,h)) the pencil genus of (X,o) (resp. a pair of (X,o) and h). In this paper, we give a method to construct pencils of compact complex curves by gluing a resolution space of (X,o) and resolution spaces of some cyclic quotient singularities. Using this, we prove some formulae on pe(X,o,h) and estimate pe(X,o). We also characterize Kodaira singularities in terms of pe(X,o,h).

• 社団法人 日本数学会の論文
• 2007-01-01

著者

• Tomaru Tadashi

  School Of Health Sciences Gunma University

関連論文

• Pencil genus for normal surface singularities
• Pinkham-Demazure construction for two dimensional cyclic quotient singularities

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