Pigeons are city birds. At home among the tall buildings, they make a mess of things where they gather in large numbers. But their synchronized movement can be mesmerizing to watch, like a school of fish in the air. What looks like an aerial performance from the ground is an act of self-preservation, defense against their urban enemies, the Red-tailed and Cooper’s hawks and peregrine falcons that also live downtown. Here’s a look at some their recent flights.