How many core genes are in the human genome?

I have no idea what you mean by ":core genes". We don't use that term in genetics or molecular biology. Many genes are allelic, such as the hemoglobin genes, of which there are at least 9 different forms. But these are not merely duplications. Different Hb genes are expressed at different times during development because they are functionally different. Burt all of the Hb genes are included in the genes that make us human.