arXiv subjects

Angelica Simonetti

Publications and source records attributed to Angelica Simonetti.

6 recordsLinked to original sources

arXiv2026

Sheaves on Graphs and their Differential Calculi

In this paper we explore the link between the theory of sheaves on graphs and noncommutative geometry showing that many concepts and constructions in the latter can be generalized and enhanced using methods coming from the former. They include notions such as Laplacians and connections, important in the theory of discrete noncommutative geometry, that are here explored with sheaf theoretic methods and using the language of (semi)simplicial sets.

math.DG↗

arXiv2026

On Gluing Data, Finite Ringed Spaces and schemes

From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link important geometric objects, such as differentiable manifolds or schemes, to certain finite ringed spaces arising from sheaves on 2 dimensional semisimplicial sets, thus opening the door to their applications in fields such as discrete differential geometry.

math.CT↗

arXiv2024

Tropical methods for stable octic double planes

This paper has been written to illustrate the power of techniques from tropical geometry and mirror symmetry for studying the KSBA moduli space of surfaces on or near the Noether line. We focus on the moduli space of octic double planes ($K^2 = 2$, $p_g = 3$) and use methods from tropical and toric geometry to classify the strata corresponding to normal KSBA-stable surfaces, focusing on the non-Gorenstein case.

math.AG↗

arXiv2023

Deformation types of Looijenga pairs of small length

Following the work already done by E. Looijenga and others, we provide an analysis of the deformation types of Looijenga (or anticanonical) pairs $(Y,D)$, where the anticanonical divisor $D$ is made of $n$ irreducible components and $6\leq n \leq9$. In doing so we also give a description of their toric models.

math.AG↗

arXiv2023

Graph Neural Networks and Time Series as Directed Graphs for Quality Recognition

Graph Neural Networks (GNNs) are becoming central in the study of time series, coupled with existing algorithms as Temporal Convolutional Networks and Recurrent Neural Networks. In this paper, we see time series themselves as directed graphs, so that their topology encodes time dependencies and we start to explore the effectiveness of GNNs architectures on them. We develop two distinct Geometric Deep Learning models, a supervised classifier and an autoencoder-like model for signal reconstruction. We apply these models on a quality recognition problem.

cs.LG↗

arXiv2022

$\mathbb{Z}/2\mathbb{Z}$-Equivariant smoothings of cusp singularities

Let $p\in X$ be the germ of a cusp singularity and let $ι$ be an antisymplectic involution, that is an involution such that there exists a nowhere vanishing holomorphic 2-form $Ω$ on $X\setminus \{p\}$ for which $ι^*(Ω)=-Ω$. Assume also that the involution is fixed point free on $X\setminus\{p\}$. We prove that a sufficient condition for such a singularity equipped with an antisymplectic involution to be equivariantly smoothable is the existence of a Looijenga (or anticanonical) pair $(Y,D)$ that admits an involution free on $Y\setminus D$ and that reverses the orientation of $D$. This work also contains the proof of an analogue necessary and sufficient condition for the $\mathbb{Z}/2\mathbb{Z}$-equivariant smoothability of simple elliptic singularities $p\in C(E)$ with $E$ an elliptic curve of degree $d\leq 8$ and even equipped with a $\mathbb{Z}/2\mathbb{Z}$-action.

math.AG↗