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

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 $\mathcal{B}(0,c_2)$.