Dynamical degrees of birational maps from indices of polynomials with respect to blow-ups II. 3D examples

Autor:	Alonso, Jaume, Suris, Yuri B., Wei, Kangning
Rok vydání:	2023
Předmět:	Mathematics - Dynamical Systems Mathematical Physics Mathematics - Algebraic Geometry Nonlinear Sciences - Exactly Solvable and Integrable Systems 37J70 14E07 39A36 14E05 14H70
Druh dokumentu:	Working Paper
Popis:	The goal of this paper is the exact computation of the degrees $\text{deg}(f^n)$ of the iterates of birational maps $f: \mathbb{P}^N \dashrightarrow \mathbb{P}^N$. In the preceding companion paper, a new method has been proposed based on the use of indices of polynomials associated to the local blow-ups used to resolve contractions of hypersurfaces by $f$, and on the control of the factorization of pull-backs of polynomials. This leads to recurrence relations for the degrees and the indices. We apply this method to several illustrative examples in three dimensions. These examples demonstrate the flexibility of the method which, in particular, does not require the construction of an algebraically stable lift of $f$, unlike the previously known methods based on the Picard group. Comment: 39 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2307.09939 Zobrazit plný text záznamu View this record from Arxiv