You accelerate air over a foil to create a negative pressure. The air on top is traveling faster than the air below. Race cars are the opposite; they accelerate air under the car to suck the car down to the ground.

Your comment about momentum of VSTOL aircraft is also correct. Its so stupid for people to say object can't hover above the ground just because the earth is spinning. The aircraft was/is spinning at the same rate as the earth, so of course it can hover and land in the exact same spot... also, in flight we take the curvature of earth into account. It's called the coriolis effect, which also affects fluids. People saying "the math doesn't work" have zero knowledge of math.