Sophie Turner Divorce -- You Take Piven, I'll Take Our Daughter ... Says Dissed Hubby

Sophie Turner -- the hot blonde model who's been linked to Jeremy Piven -- will soon be free to date openly again ... because her husband just filed for divorce ... and it looks like he's out for blood.

In the divorce docs -- obtained by TMZ -- Gianmichele Gennari wants physical and legal custody of their 7-year-old daughter, Angelica.

As we reported ... Gennari claims Turner effectively abandoned their family from time to time, choosing to hit the town till all hours of the morning ... sometimes with Piven. He says she pretended to be single -- not wearing her wedding ring -- and acted hot to trot.

Gennari wants full physical and legal custody of their child. He ONLY wants her to have monitored visits. He also wants her to pay him spousal support.