The belt broke on my AC Compressor. What is the cost for repairs?

It sounds from your description as if the air conditioning compressor failed internally and seized up, causing the serpentine belt to melt due to being dragged across a pulley that wasn't moving. The end result would have been that the belt broke, but the cause may very well be a problem with your air conditioning compressor. The compressor may be covered under your warranty, and due to the high costs that will most likely come with the appropriate repair, I would recommend you look into whether or not this item is covered. All of that being said, it would be best to have a competent technician thoroughly inspect why the belt failed, and what components will be needed to rectify the situation. It is likely that if the compressor failed internally, debris has traveled to other parts of the system, requiring further parts replacement in order to guarantee the new components will last an expected lifetime.