On the geometry of the moduli space of semi-stable plane sheaves with Hilbert polynomial P(m)=6m+3

We classify all Gieseker semi-stable sheaves on the complex projective plane that have dimension 1, multiplicity 6 and Euler characteristic 3. We show that their moduli space is birational to the blow-up at a special point of a certain moduli space of semi-stable Kronecker modules.