Meaning of “curl up” - Learner’s Dictionary

curl up

phrasal verb with curl uk us /kɜːl/ verb [ I, T ]
SIT/LIE

to sit or lie in a position with your arms and legs close to your body:

She curled up and went to sleep.
PAPER

If something flat, such as a piece of paper, curls up, the edges start to curve up.

(Definition of “curl up” from the Cambridge Learner’s Dictionary © Cambridge University Press)