How did the pigeon do? Sorry I just saw this post. Those kinds of wounds heal surprising well with Neosporin.
They need to eat birdseed mix & regular water daily. Unflavored Pedialyte with water is better than sugar water.
Hope you got the bird some help. If it was still young (not fully feathered under wings) then it is a youngster & may need some handfeeding formula, too. I've seen this happen when a young pigeon goes over to another older pigeon's space. They'll peck an intruding pigeon so it will go away, but sometimes the youngsters just cowered & try to huddle under the older adult instead of leaving, so then the adult gets mad & keeps pecking...I know, kinda nasty behavior, you'd think they'd communicate better & just tell the kid, hey this is not your nest box, get the heck out. Anyway, it happens, but it can heal, might just have a bald spot there.