  We show that the spatial dimensionality of the quantum critical point
associated with Bose--Einstein condensation at T=0 is reduced when the
underlying lattice comprises a set of layers coupled by a frustrating
interaction. Our theoretical predictions for the critical temperature as a
function of the chemical potential correspond very well with recent
measurements in BaCuSi$_{2}$O$_{6}$ [S. E. Sebastian \textit{et al}, Nature
\textbf{411}, 617 (2006)].
