  In$_2$Se$_3$ is a semiconductor material that can be stabilized in different
crystal structures (at least one 3D and several 2D layered structures have been
reported) with diverse electrical and optical properties. This feature has
plagued its characterization over the years, with reported band gaps varying in
an unacceptable range of 1 eV. Using first-principles calculations based on
density functional theory and the HSE06 hybrid functional, we investigated the
structural and electronic properties of four layered phases of In$_2$Se$_3$,
addressing their relative stability and the nature of their fundamental band
gaps, i.e., direct {\em versus} indirect. Our results show large disparities
between fundamental and optical gaps. The absorption coefficients are found to
be as high as that in direct-gap III-V semiconductors. The band alignment with
respect to conventional semiconductors indicate a tendency to $n$-type
conductivity, explaining recent experimental observations.
