Search

Let X ⊂ (H0(L)) be a smooth projective variety embedded by the complete linear system associated to a very ample line bundle L on X. We call [image omitted] the section module of L. It has been known that the syzygies of RL as R = Sym(H0(L))-module play important roles in understanding geometric properties of X [2, 3, 5, 9, 10] even if X is not projectively normal. Generalizing the case of N2, p [2, 10], we prove some uniform theorems on higher normality and syzygies of a given linearly normal variety X and general inner projections when RL satisfies property N3, p (Theorems 1.1, 1.2, and Proposition 3.1). In particular, our uniform bounds are sharp as hyperelliptic curves and elementary transforms of elliptic ruled surfaces show. [ABSTRACT FROM AUTHOR]