Paint cracking and peeling right under light


When the previous owner vacated the premisis he painted the whole house in cheap white paint. I've since noticed that the paint under the kitchen sink light is badly cracked and peeling. I can only presume it's from the exposed light bulb that is probably an inch from the ceiling. My concern is whether or not the peeling and cracking is from having a light bulb too close to the ceiling (it's a standard 60 Watt bulb) or from other reasons.
The only other reasons I can think of are 1) He turned the light on too soon after painting and the wet paint cracked and peeled from uneven drying 2) The paint is super cheap and that's just what super cheap paint does
So really my question is, should I go ahead and paint the ceiling in my kitchen will I have to face this problem if I use a good quality latex? The fixture itself is gone, it looks horrifyingly ugly anyway but that doesn't mean the replacement won't be just as close to the ceiling.
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