Projective subvarieties having large Green-Lazarsfeld index
- Authors
- Park, Euisung
- Issue Date
- 1-2월-2012
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Minimal free resolution; Green-Lazarsfeld index
- Citation
- JOURNAL OF ALGEBRA, v.351, no.1, pp.175 - 184
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF ALGEBRA
- Volume
- 351
- Number
- 1
- Start Page
- 175
- End Page
- 184
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/106085
- DOI
- 10.1016/j.jalgebra.2011.10.041
- ISSN
- 0021-8693
- Abstract
- Let X subset of P(n+c) be a nondegenerate projective irreducible subvariety of degree d and codimension c >= 1. The Green-Lazarsfeld index of X, denoted by index(X), is defined as the largest p such that the homogeneous ideal of X is generated by quadrics and the syzygies among them are generated by linear syzygies until the (p - 1)-th stage. Thus index(X) is an important invariant in order to describe the minimal free resolution of X. Recently it is shown that d = c + 1 if and only if index(X) >= c, and X is a del Pezzo variety if and only if index(X) = c - 1. In this paper, we prove that index(X) = c - 2 (c >= 3) if and only if X is either a complete intersection of three quadrics or else an arithmetically Cohen-Macaulay variety with d = c + 3 (Theorem 1.1). Also we classify X with index(X) = c - 3 (c >= 4) for the cases when d = c + 2 (Theorem 4.1) and when X is a smooth surface (Theorem 4.3). (C) 2011 Elsevier Inc. All rights reserved.
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