Antarctic cruise prices are based on people sharing a twin cabin, but these trips are equally popular with solo travellers. Somewhere between 10-20% of passengers travel on their own.
Most solo travellers choose to share a cabin (shares are always same sex). Some ships have triples or quads that make cheaper, as well as highly sociable, options.
Alternatively, it's usually possible to pay a single supplement, which is typically around 140-170% the cost of a single berth in a twin cabin, depending on the ship. Some ships also have a limited number of dedicated single cabins that cost roughly the same price, but note that these tend to book out very early.