A generic genus six curve (defined over $\mathbb{C}$) is birational to a plane sextic with four nodes. Is it possible for all such curves to have a model with no three nodes aligned? If not, is there any characteristic feature of curves where three nodes must be aligned?
The rationale of my question is the following one: if among those four nodes no three of them are aligned, it is always possible to send them in the projective plane to [0:0:1], [0:1:0], [1:0:0] and [1:1:1], using $PGL_3(\mathbb{C})$. If three nodes are aligned, it is still possible (again using $PGL_3(\mathbb{C})$ ) to send them to [0:0:1], [0:1:0], [0:1:1] and [1:0:0] but this has the drawback to yield two different models to be taken into consideration.