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- Title
On syzygies of non-complete embedding of projective varieties.
- Authors
Youngook Choi; Sijong Kwak; Euisung Park
- Abstract
Abstract  Let X be a non-degenerate, not necessarily linearly normal projective variety in $$\mathbb{P}^r$$. Recently the generalization of property N p to non-linearly normal projective varieties have been considered and its algebraic and geometric properties are studied extensively. One of the generalizations is the property N d,p for the saturated ideal I X (Eisenbud et al. in Compos Math 141: 1460â1478, 2005) and the other is the property $$N_p^S$$ for the graded module of the twisted global sections of $$\mathcal{O}_X(1)$$ (Kwak and Park in J Reine Angew Math 582: 87â105, 2005). In this paper, we are interested in the algebraic and geometric meaning of properties $$N_p^S$$ for every p ⥠0 and the syzygetic behaviors of isomorphic projections and hyperplane sections of a given variety with property $$N_p^S$$.
- Subjects
SYZYGIES (Mathematics); ISOMORPHISM (Mathematics); MATHEMATICAL analysis; MATHEMATICAL research
- Publication
Mathematische Zeitschrift, 2008, Vol 258, Issue 2, p463
- ISSN
0025-5874
- Publication type
Article