DC Field | Value | Language |
---|---|---|
dc.contributor.author | Kwak, Sijong | ko |
dc.contributor.author | Park, Jinhyung | ko |
dc.date.accessioned | 2020-03-31T08:20:09Z | - |
dc.date.available | 2020-03-31T08:20:09Z | - |
dc.date.created | 2020-03-30 | - |
dc.date.created | 2020-03-30 | - |
dc.date.created | 2020-03-30 | - |
dc.date.created | 2020-03-30 | - |
dc.date.created | 2020-03-30 | - |
dc.date.issued | 2020-04 | - |
dc.identifier.citation | ADVANCES IN MATHEMATICS, v.364 | - |
dc.identifier.issn | 0001-8708 | - |
dc.identifier.uri | http://hdl.handle.net/10203/273741 | - |
dc.description.abstract | Let X subset of P-r be a non-degenerate smooth projective variety of dimension n, codimension e, and degree d defined over an algebraically closed field of characteristic zero. In this paper, we first show that reg(O-x) <= d - e, and classify the extremal and the next to extremal cases. Our result reduces the Eisenbud-Goto regularity conjecture for the smooth case to the problem finding a Castelnuovo-type bound for normality. It is worth noting that McCullough-Peeva recently constructed counterexamples to the regularity conjecture by showing that reg(O-x) is not even bounded above by any polynomial function of d when X is not smooth. For a normality bound in the smooth case, we establish that reg(X) <= n(d - 2) + 1, which improves previous results obtained by Mumford, Bertram-Ein-Lazarsfeld, and Noma. Finally, by generalizing Mumford's method on double point divisors, we prove that reg(X) <= d - 1 + m, where m is an invariant arising from double point divisors associated to outer general projections. Using double point divisors associated to inner projections, we also obtain a slightly better bound for reg(X) under suitable assumptions. | - |
dc.language | English | - |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | - |
dc.title | A bound for Castelnuovo-Mumford regularity by double point divisors | - |
dc.type | Article | - |
dc.identifier.wosid | 000518496000002 | - |
dc.identifier.scopusid | 2-s2.0-85078410988 | - |
dc.type.rims | ART | - |
dc.citation.volume | 364 | - |
dc.citation.publicationname | ADVANCES IN MATHEMATICS | - |
dc.identifier.doi | 10.1016/j.aim.2020.107008 | - |
dc.contributor.localauthor | Kwak, Sijong | - |
dc.contributor.localauthor | Park, Jinhyung | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | Castelnuovo-Mumford regularity | - |
dc.subject.keywordAuthor | Regularity conjecture | - |
dc.subject.keywordAuthor | Double point divisor | - |
dc.subject.keywordAuthor | Projection | - |
dc.subject.keywordAuthor | Vanishing theorem | - |
dc.subject.keywordPlus | PROJECTIVE VARIETIES | - |
dc.subject.keywordPlus | GEOMETRIC-PROPERTIES | - |
dc.subject.keywordPlus | VECTOR-BUNDLES | - |
dc.subject.keywordPlus | MANIFOLDS | - |
dc.subject.keywordPlus | THEOREM | - |
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