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離散数理モデリングセミナー
過去の記録 ～06/14｜次回の予定｜今後の予定 06/15～
| 担当者 | 時弘哲治, ウィロックス ラルフ |
|---|
2024年04月24日(水)
13:30-15:00 数理科学研究科棟(駒場) 126号室
Jaume Alonso 氏 (Technische Universität Berlin)
Dynamical degrees of birational maps from indices of polynomials with respect to blow-ups (English)
Jaume Alonso 氏 (Technische Universität Berlin)
Dynamical degrees of birational maps from indices of polynomials with respect to blow-ups (English)
[ 講演概要 ]
In this talk we propose a new method for the exact computation of the degree $\deg (f^n)$ of the iterates of a birational map $f:\mathbb{P}^n \dashrightarrow \mathbb{P}^n$. The method is based on two main ingredients. Firstly, the factorisation of a polynomial under the pull-back by $f$, based on local indices of a polynomial associated to blow-ups used to resolve the singularity. Secondly, the propagation of these indices along the orbits of $f$. We will illustrate the method in different examples, showing its flexibility, since it does not require the construction of an algebraically stable lift of $f$, unlike other methods based on the Picard group.
This is a joint work with Yuri Suris and Kangning Wei.
In this talk we propose a new method for the exact computation of the degree $\deg (f^n)$ of the iterates of a birational map $f:\mathbb{P}^n \dashrightarrow \mathbb{P}^n$. The method is based on two main ingredients. Firstly, the factorisation of a polynomial under the pull-back by $f$, based on local indices of a polynomial associated to blow-ups used to resolve the singularity. Secondly, the propagation of these indices along the orbits of $f$. We will illustrate the method in different examples, showing its flexibility, since it does not require the construction of an algebraically stable lift of $f$, unlike other methods based on the Picard group.
This is a joint work with Yuri Suris and Kangning Wei.
