  The Gauge-Including Projector Augmented Wave (GIPAW) method, within the
Density Functional Theory (DFT) Generalized Gradient Approximation (GGA)
framework, is applied to compute solid state NMR parameters for $^{27}Al$ in
the $\alpha$, $\theta$, and $\kappa$ aluminium oxide phases and their gibbsite
and boehmite precursors. The results for well-established crystalline phases
compare very well with available experimental data and provide confidence in
the accuracy of the method. For $\gamma$-alumina, four structural models
proposed in the literature are discussed in terms of their ability to reproduce
the experimental spectra also reported in the literature. Among the considered
models, the $Fd\bar{3}m$ structure proposed by Paglia {\it et al.} [Phys. Rev.
B {\bf 71}, 224115 (2005)] shows the best agreement. We attempt to link the
theoretical NMR parameters to the local geometry. Chemical shifts depend on
coordination number but no further correlation is found with geometrical
parameters. Instead our calculations reveal that, within a given coordination
number, a linear correlation exists between chemical shifts and Born effective
charges.
