Moduli of Rank 3 Semistable Sheaves on the Projective Space P3 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 P3, 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.