Shard Realms (called "Fragmenti" by older mages) are umbral realms connected to one of the nine spheres and mapping over one of the planets of the solar system.
In the terms of the Celestial Chorus, every Shard Realm is a fraction of the One. A Shard Realm is connected to one of the planets within the Solar system and form its own specific Umbra. Each Shard Realm is connected to a specific Sphere that is dominant within its boundaries. Every Shard Realm is also connected to a Shade Realm, which is rumored to lead into a parallel universe dominated by one of the Spheres. Each Shard Realm is inhabited and ruled by a powerful Celestine.
Modern terminology usually refers to the Shard Realm simply as the associated celestial body.