1. Rub inside of a 4-quart heavy pot with cut sides of garlic, then discard garlic. Add wine to pot and bring just to a simmer over moderate heat.
2. Gradually add cheese to pot and cook, stirring constantly in a zigzag pattern (not a circular motion) to prevent cheese from balling up, until cheese is just melted and creamy (do not let boil). Stir cornstarch mixture again and stir into fondue. Bring fondue to a simmer and cook, stirring, until thickened, 5 to 8 minutes. Transfer to fondue pot set over a flame.