On the Canonical Rings of Some Horikawa Surfaces. Part I (original) (raw)

This paper is devoted to finding necessary and sufficient conditions for a graded ring to be the canonical ring of a minimal surface of general type with K2 = 2pg-3, pg > 3, and such that its canonical linear system has one base point. 1. Known results. 1.1. Let 5 be a minimal surface of general type with K2 = 2pg-3, pg > 3. We assume that the canonical linear system \K\ of S has one base point P. Following Horikawa [4, Lemma 2] let ir: S'-► 5 be the quadratic transformation with center P and exceptional curve E.