On syzygies, degree, and geometric properties of projective schemes with property N-3,N-p

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dc.contributor.authorAhn, Jeamanko
dc.contributor.authorKwak, Sijongko
dc.date.accessioned2015-04-07T05:09:29Z-
dc.date.available2015-04-07T05:09:29Z-
dc.date.created2015-02-10-
dc.date.created2015-02-10-
dc.date.issued2015-07-
dc.identifier.citationJOURNAL OF PURE AND APPLIED ALGEBRA, v.219, no.7, pp.2724 - 2739-
dc.identifier.issn0022-4049-
dc.identifier.urihttp://hdl.handle.net/10203/195284-
dc.description.abstractLet X be a reduced, but not necessarily irreducible closed subscheme of codimension e in a projective space. One says that X satisfies property N-d,N-p (d >= 2) if the i-th syzygies of the homogeneous coordinate ring are generated by elements of degree < d i for 0 <= i <= p (see [10] for details). Much attention has been paid to linear syzygies of quadratic schemes (d = 2) and their geometric interpretations (cf. [1,9, 15-17]). However, not very much is actually known about algebraic sets satisfying property N-d,N-p, d >= 3. Assuming property N-d,N-e, we give a sharp upper bound deg (X) <= ((e+d-1)(d-1)). It is natural to ask whether deg(X) = ((e+d-1)(d-1)) implies that e) X is arithmetically Cohen-Macaulay (ACM) with a d-linear resolution. In case of d = 3, by using the elimination mapping cone sequence and the generic initial ideal theory, we show that deg(X) = ((e+2)(2)) if and only if X is ACM with a 3-linear 2 resolution. This is a generalization of the results of Eisenbud et al. (d = 2) [9,10]. We also give more general inequality concerning the length of the finite intersection of X with a linear space of not necessary complementary dimension in terms of graded Betti numbers. Concrete examples are given to explain our results.-
dc.languageEnglish-
dc.publisherELSEVIER SCIENCE BV-
dc.subjectGENERIC INITIAL IDEALS-
dc.subjectRESOLUTIONS-
dc.subjectVARIETIES-
dc.titleOn syzygies, degree, and geometric properties of projective schemes with property N-3,N-p-
dc.typeArticle-
dc.identifier.wosid000351248100013-
dc.identifier.scopusid2-s2.0-84925014372-
dc.type.rimsART-
dc.citation.volume219-
dc.citation.issue7-
dc.citation.beginningpage2724-
dc.citation.endingpage2739-
dc.citation.publicationnameJOURNAL OF PURE AND APPLIED ALGEBRA-
dc.identifier.doi10.1016/j.jpaa.2014.09.024-
dc.contributor.localauthorKwak, Sijong-
dc.contributor.nonIdAuthorAhn, Jeaman-
dc.type.journalArticleArticle-
dc.subject.keywordPlusGENERIC INITIAL IDEALS-
dc.subject.keywordPlusRESOLUTIONS-
dc.subject.keywordPlusVARIETIES-
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