Rub inside of a 4-quart heavy pot with cut sides of garlic, then discard or set aside garlic. Add wine to pot and bring just to a simmer over moderate heat. (You may as well enjoy a glass at this time.).
Mix cornstarch with shredded cheese and gradually add cheese to pot and cook, stirring constantly in a zig zag pattern (rather than circular motion) until cheese is melted and creamy. Don't let the cheese boil if you can help it.
If the fondue is still lumpy after the cheese melts, adding a few drops of lemon juice will help.
Bring fondue to simmer and cook, stirring, until thickened, 5 to 8 minutes.
Transfer to fondue pot. Good dipping options are bread cubes, potatoes, broccoli, or apple slices.