We analyze $^{12}$CO($J$=2-1), $^{13}$CO($J$=2-1), C$^{18}$O ($J$=2-1), and 1.3 mm continuum maps of the $rho$ Ophiuchi A photo-dissociation region (PDR) obtained with ALMA. Layered structures of the three CO isotopologues with an angular separation of 10 arcsec = 6.6$times$10$^{-3}$ pc = 1400 au are clearly detected around the Be star, S1 (i.e., each front of emission shifts from the near to far side in order of $^{12}$CO, $^{13}$CO, and C$^{18}$O). We estimate the spatial variations of $X$($^{13}$CO)/$X$(C$^{18}$O) abundance ratios, and find that the abundance ratio is as high as 40 near the emission front, and decreases to the typical value in the solar system of 5.5 in a small angular scale of 4 arcsec = 2.6$times$10$^{-3}$ pc = 560 au. We also find that the $I$($^{12}$CO(2-1))/$I$($^{13}$CO(2-1)) intensity ratio is very high ($>$21) in the flat-spectrum young stellar object, GY-51, located in the PDR. The enhancement of the ratios indicates that the UV radiation significantly affects the CO isotopologues via selective dissociation in the overall $rho$ Ophiuchi A PDR, and that the $rho$ Ophiuchi A PDR has a plane-parallel structure.
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