Di Carlo left after Chievo took just three points from 18 games.
The club lost 4-1 at Palermo at the weekend, but Corini is relatively inexperienced at the top level.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.