I read Frederic Delavier’s book « Strength Training Anatomy » and there is good stuff about barbell curls.
Standing with your back straight, take the barbell with a supinated grip and your hands are wider than your shoulders :
Inhale and flex your arms with an isometric contraction of your glutes, abs and spinal to not swinging your torso.
Exhale at the end of the movement
This exercise works mostly biceps, brachialis and a little bit the brachioradialis, the pronator teres and all the flexors of wrist and fingers.
When you change the spacing hands, you work deeply different part :
Widely spaced hands = short head of the biceps
Very close hands = long head of the biceps
When you raise elbows at the end of flexion, you increase biceps contraction and you work the anterior deltoids.
You can do this exercise in a strict way with your back to the wall without lifting your shoulder blades.