The more important question is what is the height of the base of the nut slots compared to the first two frets (ie zero fret + first fret) . If the nut slots are higher than the first frets the slots need to be filed lower.
As Louie says, the frets , including the zero fret are all supposed to be on the same plane. The nut slots can be filed down as far as you want ... the lower the better ... as long as the slots are lower than the frets, all is good.
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