Nocere is the second stage of Singularis, and is triggered (set off) by a traumatic event in the Singulari's childhood. Nocere advances from Filios, the harmless first stage of Singularis.
Depending on the ability the Singulari has, the downsides will vary. There are no universal downsides, but some negative side effects are shared across different abilities.
You can read up about Abilities
here, and about Nocere and Filios
here.
Hope this helps!