Irreducibility conjecture for the moduli space of stable bundles on a quintic surface

Let $X\subset \mathbb{P}^3$ be a very general quintic surface, and let $M_X(2,1,10)$ denote the moduli space of stable bundles on $X$ of rank $2$, degree $1$, and second Chern class $c_2=10$. Irreducibility conjecture. The moduli space

$$M_X(2,1,10)$$

is irreducible. The paper establishes a single irreducible component for bundles with seminatural cohomology and places this case in the range where the moduli space is generically smooth of the expected dimension; irreducibility for $c_2=10$ remains open in the supplied text.