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Discrete mathematical modelling seminar
Seminar information archive ～05/02｜Next seminar｜Future seminars 05/03～
| Organizer(s) | Tetsuji Tokihiro, Ralph Willox |
|---|
2024/04/24
13:30-15:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Jaume Alonso (Technische Universität Berlin)
Dynamical degrees of birational maps from indices of polynomials with respect to blow-ups (English)
Jaume Alonso (Technische Universität Berlin)
Dynamical degrees of birational maps from indices of polynomials with respect to blow-ups (English)
[ Abstract ]
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.
