Castelnuovo-Mumford regularity bounds for singular surfaces

We prove the regularity conjecture, namely Eisenbud-Goto conjecture, for a normal surface with rational, Gorenstein elliptic and log canonical singularities. Along the way, we bound the regularity for a dimension zero scheme by its Loewy length and for a curve allowing embedded or isolated point components by its arithmetic degree.
Comment: 11 pages, title changed; Mathematische Zeitschrift, 2015