In answer to the question "why do the corners lift when using ABS", the answer has to do with the coefficient of thermal expansion (or contraction).
ABS, compared to PLA, has a higher coefficient meaning that as the temperature of you part changes the more the part will deform. With 3d printing, the material extruded from the nozzle is quite a bit higher than the build chamber. As the layers print and the extruder moves up, the lowest layers are cooler than the layers above, shrinking as time goes on.
For angular parts this is a larger problem than for round parts. With angular parts (parts with sharp edges in X and Y axis) as they cool, the internal stresses induced by cooling increase and can't be resolved in just the xy axis and cannot move into the build plate. The part then lifts up to reduce these stresses.
A brim or raft, is a thin layer that ideally cools at a constant rate through out which will effectively increase the bonding of your part to the build plate. Abs to abs bonding being stronger than abs bonding to whatever your build plate material surface is. For most parts this is sufficient to keep good adhesion while your part builds and cools. Raises the temperature of the build plate also reduced the stress in the brim/raft by reducing the difference in temperature. This is why those are the go-to solutions for stopping abs from lifting.
If your part is large enough or the angles are quite sharp in XY, (think of a five pointed star for example). Then the brim raft won't necessarily be enough to prevent the warping. That's where "helper discs" "mouse ears" etc . Are helpful. These, when dispersed around the outer sharp corners, increase the surface area of the raft and also reduce the angles of the thermal contraction due to cooling.
Note, that while I'm talking about ABS specifically, this will apply to any and all materials if the part geometry, or material properties have the same issues. Nylon for example is also a pain to print for similar reasons.
The final thing to say is that all if this is for nothing if your build plate isn't both flat and level.