No bb curls are not a core lift. Neither are skull crushers or bent over rows. A core lift is a compound movement that recruits multiple muscle groups during the exercise(deadlift, power clean, bench, squat). It's not "working the core of the muscle" as it sounds like you're interpreting it with "bicep core lift." BB curls are an isolation exercise. However the way people do them in my gym, you could arguably call them a core lift because of how much lower back and swinging is involved.
Here it is straight off a website:
Explain the difference between Core lifts and Auxiliary lifts.
Core lifts - any lift that uses the major muscle groups or a lift that uses multi-jointed effort during the lift. Usually a large group of muscles are at work
Examples: Bench press, Squats, Power cleans, Push press.
Auxiliary lifts - any minor muscle group. Usually a small group or individual muscles.
Example: Arm curls, Triceps extensions, Leg curls, Leg extensions.
http://www.geocities.com/HotSprings/Villa/4787/EXERCISE.htm
Close grip presses are done on either flat or incline bench. Instead of the normal, wider grip that you use when you bench, you move your hands in closer to each on the bar. This causes the triceps to get targeted more.