curly has no recorded synonym. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is straight.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
(of hair) having curls or waves
“they envied her naturally curly hair”
Synonyms, antonyms and the broader and narrower relations for curly come from Princeton University’s WordNet. Full sources and licences.