3 papers
math.AG2026
The Calculus of Blowups on a Ruled Surface
Richard A. P. Birkett
The purposes of this article are threefold. First, to determine numerically when an arbitrary blowup of a smooth surface is smooth. We show the surface is smooth if and only if cer…
math.DS2024
Algebraic Stability for Skew Products
Richard A. P. Birkett
In this article we study algebraic stability for rational skew products in two dimensions , i.e. maps of the form . We prove…
math.DS2023
Skew Products on the Berkovich Projective Line
Richard A. P. Birkett
In this article, we develop a dynamical theory for what shall be called a skew product on the Berkovich projective line, $ϕ_*: \mathbb{P}^1_{\text{an}}(K) \to \mathbb{P}^1_{\text{a…