Curl is built into any item that has any version of stockinette stitch right to its edges, where those edges are not stabilized by being sewn into seams. It's structural, and it causes the bottom and top edges to roll towards the right side of the item, and the side edges to roll towards the wrong side. (TechKnitter wrote on the subject, if you wish to study it in detail...)
|Purple swatch - Wrong Side|
A swatch told me that if I added ribbing at the ends, and along the edges, I could cure the curl.
Compare the left and top (curling) and right and bottom (ribbed) edges.
I made the entire shawl like this. I will not bore you with the technical difficulties overcome, or the mistakes that had to be fixed/fudged. There were several of each. In the end, I had a cushy, seafoam greeny blue coloured shawl, with more or less flat sides (we can live with their occasional tendency to fold back to the wrong side), lovely corners and ribbed ends.