We show that the moduli space of semi-stable sheaves on a smooth quadric surface, having dimension $1$, multiplicity $4$, Euler characteristic $2$, and first Chern class $(2, 2)$, is the blow-up at two points of a certain hypersurface in a weighted projective space.
"On two moduli spaces of sheaves supported on quadric surfaces." Osaka J. Math. 54 (2) 323 - 333, April 2017.