Public Works are structures and real-estate granted to a planet by a House. They are a permanent and effective method of gaining influence on a planet.
In addition to building income-generating or other useful facilities on a planet, you can also boost your influence considerably by commissioning public works. These are expensive works that serve the good of the planetary populace, and their creation will bring a rise in popularity and hence in influence for your House. The work is named as you see fit, and cannot be destroyed - the populace is assumed to rebuild them in the event of a destructive event. Public Works have no in-game effect other than to grant an influence boost. The works available to build are listed below, together with the average build price. Note that there is no cost to maintain a Public Work, any such burden is taken on by the local Government or volunteers from the population.
Since the influence boost from construction of a public work reflects appreciation of the work by the populace, there is a rule of diminishing returns in place when it comes to building multiple public works on the same planet. The influence gain you will receive is considerably less for the second and subsequent public works on a planet, and if the same House builds many works there, that House will receive little or no benefit once the first few works are in place. This reflects the fact that once such works become commonplace, the impact of a new public work on the populace is much less apparent - “Oh, House <xxx> built another monument? Big deal”.
You can view the public works on a planet and commission new ones by following the 'Public Works' link from the main Planetary Information Panel for a planet (see section 3.2 below).
as seen in the Rulebook
—————————Description of Public Work——————————-