Definition of curl up phrasal verb from the Oxford Advanced Learner's Dictionary

  

curl up

 phrasal verb
phrasal verb
 
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Phrasal Verbs
 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.

curl up

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curl somebody up

 
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(British English, informal) to become or make somebody become very embarrassed

curl up

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curl somethingup

 
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 to form or make something form into a tightly curled shape The paper started to shrivel and curl up in the heat.
See the Oxford Advanced American Dictionary entry: curl up