New irreducible components of $\mathcal{B}(0,c_2)$ and Computation of the Dimension of its tangent space

TL;DR

This paper introduces a Macaulay2 code to compute tangent space dimensions of certain moduli spaces, identifies components with singular points, and proves the existence of infinite irreducible components of these spaces.

Contribution

It provides computational tools and theoretical results on the structure and components of the moduli space al{B}(0,c_2), including new irreducible components.

Findings

Computed tangent space dimensions for specific cases.

Identified components containing singular points.

Proved existence of infinite families of irreducible components.

Abstract

We provide a Macaulay2 code for computing the dimension of the tangent space to $\mathcal{B}(e,c_2)$ in certain cases. Using this code, we identify components of $\mathcal{B}(e,c_2)$ containing singular points and compute the dimension of the irreducible component $M_4$ of $\mathcal{B}(-1,6)$, whose existence was proved in \cite{MF2021}. Furthermore, we prove the existence of infinite families of irreducible components of $\mathcal{B}(0,c_2)$.