  We prove that two cusps of the same dimension in the Baily-Borel
compactification of some classical series of modular varieties are linearly
dependent in the rational Chow group of the compactification. This gives a
higher dimensional analogue of the Manin-Drinfeld theorem. As a consequence, we
obtain a higher dimensional generalization of modular units as higher Chow
cycles on the modular variety.
