Alessio Caminata

collaborators

3 papers

math.AC2025

Hilbert-Kunz series, F-signature series, and weak p-fractals

Alessio Caminata, Francesco Zerman

We extend the theory of $p$ -fractals of Monsky and Teixeira by introducing the notion of weak $p$ -fractal. We prove that for a hypersurface $f$ having rational Hilbert-Kunz series…

cs.SC2025

Solving Polynomial Systems with Gröbner Bases: An Introduction to F4 and FGLM

Anna Maria Bigatti, Alessio Caminata, Tor Kristian Ellingsen +3

These notes originate from a reading course held by the authors in the spring of 2024 at the Università di Genova. They provide a hands-on introduction to the F4 and FGLM algorithm…

math.AC2024

F-signature functions of diagonal hypersurfaces

Alessio Caminata, Samuel Shideler, Kevin Tucker +1

Let $f$ be a diagonal hypersurface in $A_{p} = F_{p} [[x_{1}, \dots, x_{n}]]$ . We study the behavior of the function $ϕ_{f,p}({a}/{p^e})=p^{-ne}\dim_{\mathbb{F}_p}\big(A_p/(x_1^{p^e},\…