Depends on how minor they are. I've had fair results with automotive polishes and rubbing compounds, but if the scratches are deeper you will need professional grade polishing pads and power equipment. I bought a set of furniture grade polishing pads for my 5" random orbital sander, ranging from 800 to 4000 grit, and those can polish darn near anything to a high gloss. Works great on the Corian - I have brought a semi-gloss top to full gloss and have also removed fairly deep scratches with them.
You can find these polishing pads in most woodworker supply catalogs or web sites.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL