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複素解析幾何セミナー
過去の記録 ～06/28｜次回の予定｜今後の予定 06/29～
| 開催情報 | 月曜日 10:30～12:00 数理科学研究科棟(駒場) 126号室 |
|---|---|
| 担当者 | 平地 健吾, 高山 茂晴 |
2026年07月13日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
神田 秀峰 氏 (東京大学)
Holomorphic polynomial crystallographic actions of nilpotent groups (Japanese)
https://forms.gle/8ERsVDLuKHwbVzm57
神田 秀峰 氏 (東京大学)
Holomorphic polynomial crystallographic actions of nilpotent groups (Japanese)
[ 講演概要 ]
It is a natural and still open question whether every simply connected nilpotent Lie group endowed with a left-invariant complex structure is biholomorphic to $\mathbb{C}^n$. In this talk, we give an affirmative answer under the additional assumption that the complex structure is nilpotent. Moreover, we construct such a biholomorphism explicitly by polynomial maps in exponential coordinates. As a consequence, every lattice in such a Lie group admits a free, properly discontinuous and cocompact action on $\mathbb{C}^n$ by holomorphic polynomial automorphisms. We interpret this as a holomorphic analogue of polynomial crystallographic actions, namely actions on $\mathbb{R}^n$ by polynomial diffeomorphisms that are free, properly discontinuous and cocompact, as introduced by Dekimpe, Igodt, and Lee.
[ 参考URL ]It is a natural and still open question whether every simply connected nilpotent Lie group endowed with a left-invariant complex structure is biholomorphic to $\mathbb{C}^n$. In this talk, we give an affirmative answer under the additional assumption that the complex structure is nilpotent. Moreover, we construct such a biholomorphism explicitly by polynomial maps in exponential coordinates. As a consequence, every lattice in such a Lie group admits a free, properly discontinuous and cocompact action on $\mathbb{C}^n$ by holomorphic polynomial automorphisms. We interpret this as a holomorphic analogue of polynomial crystallographic actions, namely actions on $\mathbb{R}^n$ by polynomial diffeomorphisms that are free, properly discontinuous and cocompact, as introduced by Dekimpe, Igodt, and Lee.
https://forms.gle/8ERsVDLuKHwbVzm57
