Alessio Caminata

activity

20152025

most citedA Pascal's Theorem for rational normal curves

6 citations · 17 across the 10 of their papers we have counts for

collaborators

16 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…

math.AG2024

Simplices osculating rational normal curves

Alessio Caminata, Enrico Carlini, Luca Schaffler

A classical result of von Staudt states that if eight planes osculate a twisted cubic curve and we divide them into two groups of four, then the eight vertices of the corresponding…

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.AG2022

Determinantal varieties from point configurations on hypersurfaces

Alessio Caminata, Han-Bom Moon, Luca Schaffler

We consider the scheme $X_{r, d, n}$ parametrizing $n$ ordered points in projective space $P^{r}$ that lie on a common hypersurface of degree $d$ . We show that this scheme has…

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.AG2020★ 4 cited

Point configurations, phylogenetic trees, and dissimilarity vectors

Alessio Caminata, Noah Giansiracusa, Han-Bom Moon +1

In 2004 Pachter and Speyer introduced the higher dissimilarity maps for phylogenetic trees and asked two important questions about their relation to the tropical Grassmannian. Mult…

math.AC2019

Isolated singularities with large class group

Alessio Caminata

Let $d \geq 3$ and $g \geq 1$ be integers. Using a geometric construction involving the symmetric product of a projective curve, we exhibit a $d$ -dimensional complete local normal doma…

math.AG2019★ 6 cited

A Pascal's Theorem for rational normal curves

Alessio Caminata, Luca Schaffler

Pascal's Theorem gives a synthetic geometric condition for six points $a, \dots, f$ in $P^{2}$ to lie on a conic. Namely, that the intersection points $\overline{ab}\cap\over…

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.AC2017

Differential symmetric signature in high dimension

Holger Brenner, Alessio Caminata

We study the differential symmetric signature, an invariant of rings of finite type over a field, introduced in a previous work by the authors in an attempt to find a characteristi…

math.AG2017

Equations for point configurations to lie on a rational normal curve

Alessio Caminata, Noah Giansiracusa, Han-Bom Moon +1

The parameter space of $n$ ordered points in projective $d$ -space that lie on a rational normal curve admits a natural compactification by taking the Zariski closure in $(\mathbb{P…

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…

math.AC2016★ 3 cited

The Symmetric signature of cyclic quotient singularities

Alessio Caminata, Lukas Katthän

The symmetric signature is an invariant of local domains which was recently introduced by Brenner and the first author in an attempt to find a replacement for the $F$ -signature in…

math.AC2016

The symmetric signature

Holger Brenner, Alessio Caminata

We define two related invariants for a $d$ -dimensional local ring $(R, m, k)$ called syzygy and differential symmetric signature by looking at the maximal free splitting o…

math.AC2015★ 4 cited

Generalized Hilbert-Kunz function in graded dimension two

Holger Brenner, Alessio Caminata

We prove that the generalized Hilbert-Kunz function of a graded module $M$ over a two-dimensional standard graded normal $K$ -domain over an algebraically closed field $K$ of prime…

math.AC2015

Cohomological dimension and arithmetical rank of some determinantal ideals

Davide Bolognini, Alessio Caminata, Antonio Macchia +1

Let $M$ be a $(2 \times n)$ non-generic matrix of linear forms in a polynomial ring. For large classes of such matrices, we compute the cohomological dimension (cd) and the arithme…