Castelnuovo-Mumford regularity bounds for singular surfaces

Abstract

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.

arXiv comment11 pages, title changed; Mathematische Zeitschrift, 2015