Matteo Ruggiero

collaborators

3 papers

math.DS2026

On the dynamical Manin-Mumford conjecture for plane polynomial maps

Romain Dujardin, Charles Favre, Matteo Ruggiero

We prove the dynamical Manin-Mumford conjecture for regular polynomial maps of A^2 and irreducible curves avoiding super-attracting orbits at infinity, over any field of characteri…

math.AG2025

Strict germs on normal surface singularities

Matteo Ruggiero

We show that any holomorphic germ $f : (X, x_{0}) \to (Y, y_{0})$ of topological degree $1$ between normal surface singularities can be written as $f = I ¨ \circ I ¨ $ , where $Ï\colon Y'…

math.DS2025

Polynomial skew products with small relative degree

Romain Dujardin, Charles Favre, Matteo Ruggiero

We investigate the local dynamics of a proper superattracting holomorphic germ $f$ in $(C^{2}, 0)$ possessing a totally invariant line $L$ such that $f^{*} L = d L$ with $d\ge 2…