I .
curl up | be ˌcurled ˈup
to lie or sit with your back curved and your arms and legs bent close to your body :
She curled up and closed her eyes.
II .
curl up | ˌcurl sb ˈup
( BrE , informal ) to become or make sb become very embarrassed
III .
curl up | ˌcurl sth ↔ ˈup
to form or make sth form into a tightly curled shape :
The paper started to shrivel and curl up in the heat.