Typically these cracks form in the shape of a "Y" and they are called "crow's feet" though sometimes they are just straight cracks. They get packed full of polish and or wax and stand out like a sore thumb on an otherwise perfectly finished car.
"Lacquer checking" is a different phenomenon but not that unlike what the OP has going on. Below is a photo of lacquer checking.
I did some testing on this particular car to see just how deep the lacquer checking goes. I wet sanded until I got to the bottom of the "Depth of checking" and found that it goes about half way through the primer's film build. After my testing, I was obviously left with a big "clam shell" of an area with no paint. The clam shell was taped around and filled with primer surfacer and sanded flat before being repainted.