  The band offsets and the chemical bonding at the interfaces between (-201)
$\beta$-Ga$_2$O$_3$ and Al$_2$O$_3$ polymorphs are studied through hybrid
functional calculations. For alumina, we consider four representative phases,
i.e., $\alpha$, $\kappa$, $\theta$ and $\gamma$-Al$_2$O$_3$. We generate
realistic slab models for the interfaces which satisfy electron counting rules.
The O atoms bridge the $\beta$-Ga$_2$O$_3$ and Al$_2$O$_3$ slabs and all the
dangling bonds are saturated. The band offsets are obtained by applying an
alignment scheme which requires separate bulk and interface calculations. The
calculated band offsets are useful for the design of devices based on the
$\beta$-Ga$_2$O$_3$/Al$_2$O$_3$heterojunctions, particularly
$\beta$-Ga$_2$O$_3$ metal-oxide semiconductor field effect transistors.
