Alessio Caminata

activity

20162025

collaborators

Showing math.ACShow all

5 papers · 1 filter

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…

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},\…

math.AC2020

Nearly Gorenstein cyclic quotient singularities

Alessio Caminata, Francesco Strazzanti

We investigate the nearly Gorenstein property among $d$ -dimensional cyclic quotient singularities $k [[x_{1}, \dots, x_{d}]]^{G}$ , where $k$ is an algebraically closed field and $G\…

math.AC2018

F-signature function of quotient singularities

Alessio Caminata, Alessandro De Stefani

We study the shape of the F-signature function of a $d$ -dimensional quotient singularity $k [[x_{1}, \dots, x_{d}]]^{G}$ , and we show that it is a quasi-polynomial. We prove that…

math.AC2016

The symmetric signature

Alessio Caminata

This is the author's Ph.D. thesis. We introduce two related invariants for local (and standard graded) rings called differential and syzygy symmetric signature. These are defined b…