Moduli of Rank 3 Semistable Sheaves on the Projective Space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {𝕇}^{3} $\end{document} with Singularities of Mixed Dimension

Studying the Gieseker–Maruyama moduli space of normalized semistable coherent rank 3 sheaves of positive second Chern class and nonnegative third Chern class on the projective space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {𝕇}^{3} $\end{document}, we find the first example of an irreducible component of this moduli space with small values of Chern classes in which the generic sheaf has singularities of mixed dimension: zero- and one-dimensional singularities simultaneously. Previously, some examples of components of moduli of semistable sheaves with singularities of mixed dimension were constructed only for rank 2 sheaves by Ivanov and Tikhomirov in 2018 as well as by Almeida, Jardim, and Tikhomirov in 2022.