While they may look troublesome, curled edges are not uncommon and do not necessarily detract from the value of your rug.
curled edges usually are usually caused by hanging the carpet for an extended time, way in which carpet had been stored ("barrel rolled,") or because of too much/ little tension within the skeleton of the rug.
These curls usually flatten within several weeks of use. A professional steaming by your local oriental rug retailer may help. More commonly, a thick strap (either vinyl or leather) is applied to the back of the rug to either prevent or fix this issue. The last resort would be to have a professional block the rug on a bed of needles and starch it.