Projective subvarieties having large Green-Lazarsfeld index
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Park, Euisung | - |
dc.date.accessioned | 2021-09-06T10:17:46Z | - |
dc.date.available | 2021-09-06T10:17:46Z | - |
dc.date.created | 2021-06-19 | - |
dc.date.issued | 2012-02-01 | - |
dc.identifier.issn | 0021-8693 | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/106085 | - |
dc.description.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. | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | - |
dc.subject | MINIMAL DEGREE | - |
dc.subject | VARIETIES | - |
dc.subject | CURVES | - |
dc.subject | SURFACES | - |
dc.subject | SYZYGIES | - |
dc.subject | SCROLLS | - |
dc.title | Projective subvarieties having large Green-Lazarsfeld index | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Park, Euisung | - |
dc.identifier.doi | 10.1016/j.jalgebra.2011.10.041 | - |
dc.identifier.scopusid | 2-s2.0-84455205531 | - |
dc.identifier.wosid | 000299599300007 | - |
dc.identifier.bibliographicCitation | JOURNAL OF ALGEBRA, v.351, no.1, pp.175 - 184 | - |
dc.relation.isPartOf | JOURNAL OF ALGEBRA | - |
dc.citation.title | JOURNAL OF ALGEBRA | - |
dc.citation.volume | 351 | - |
dc.citation.number | 1 | - |
dc.citation.startPage | 175 | - |
dc.citation.endPage | 184 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.subject.keywordPlus | MINIMAL DEGREE | - |
dc.subject.keywordPlus | VARIETIES | - |
dc.subject.keywordPlus | CURVES | - |
dc.subject.keywordPlus | SURFACES | - |
dc.subject.keywordPlus | SYZYGIES | - |
dc.subject.keywordPlus | SCROLLS | - |
dc.subject.keywordAuthor | Minimal free resolution | - |
dc.subject.keywordAuthor | Green-Lazarsfeld index | - |
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