Moduli of rank 3 semistable sheaves on the projective space ${\Bbb P}^3$ 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 ${\Bbb P}^3$, 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.