DC Field | Value | Language |
---|---|---|
dc.contributor.author | Ahn, Jeaman | ko |
dc.contributor.author | Kwak, Sijong | ko |
dc.date.accessioned | 2015-04-07T05:09:29Z | - |
dc.date.available | 2015-04-07T05:09:29Z | - |
dc.date.created | 2015-02-10 | - |
dc.date.created | 2015-02-10 | - |
dc.date.issued | 2015-07 | - |
dc.identifier.citation | JOURNAL OF PURE AND APPLIED ALGEBRA, v.219, no.7, pp.2724 - 2739 | - |
dc.identifier.issn | 0022-4049 | - |
dc.identifier.uri | http://hdl.handle.net/10203/195284 | - |
dc.description.abstract | Let 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.language | English | - |
dc.publisher | ELSEVIER SCIENCE BV | - |
dc.subject | GENERIC INITIAL IDEALS | - |
dc.subject | RESOLUTIONS | - |
dc.subject | VARIETIES | - |
dc.title | On syzygies, degree, and geometric properties of projective schemes with property N-3,N-p | - |
dc.type | Article | - |
dc.identifier.wosid | 000351248100013 | - |
dc.identifier.scopusid | 2-s2.0-84925014372 | - |
dc.type.rims | ART | - |
dc.citation.volume | 219 | - |
dc.citation.issue | 7 | - |
dc.citation.beginningpage | 2724 | - |
dc.citation.endingpage | 2739 | - |
dc.citation.publicationname | JOURNAL OF PURE AND APPLIED ALGEBRA | - |
dc.identifier.doi | 10.1016/j.jpaa.2014.09.024 | - |
dc.contributor.localauthor | Kwak, Sijong | - |
dc.contributor.nonIdAuthor | Ahn, Jeaman | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordPlus | GENERIC INITIAL IDEALS | - |
dc.subject.keywordPlus | RESOLUTIONS | - |
dc.subject.keywordPlus | VARIETIES | - |
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