dc.identifier.uri |
http://dx.doi.org/10.15488/2702 |
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dc.identifier.uri |
http://www.repo.uni-hannover.de/handle/123456789/2728 |
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dc.contributor.author |
Eisenbud, David
|
|
dc.contributor.author |
Green, Mark
|
|
dc.contributor.author |
Hulek, Klaus
|
|
dc.contributor.author |
Popescu, Sorin
|
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dc.date.accessioned |
2018-01-29T14:34:06Z |
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dc.date.available |
2018-01-29T14:34:06Z |
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dc.date.issued |
2005 |
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dc.identifier.citation |
Eisenbud, D.; Green, M.; Hulek, K.; Popescu, S.: Restricting linear syzygies: Algebra and geometry. In: Compositio Mathematica 141 (2005), Nr. 6, S. 1460-1478. DOI: https://doi.org/10.1112/S0010437X05001776 |
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dc.description.abstract |
Let X ⊂ ℙr be a closed scheme in projective space whose homogeneous ideal is generated by quadrics. We say that X (or its ideal I X) satisfies the condition N2,p if the syzygies of I X are linear for p steps. We show that if X satisfies N2,p then a zero-dimensional or one-dimensional intersection of X with a plane of dimension ≤ p is 2-regular. This extends a result of Green and Lazarsfeld. We give conditions when the syzygies of X restrict to the syzygies of the intersection. Many of our results also work for ideals generated by forms of higher degree. As applications, we bound the p for which some well-known projective varieties satisfy N2,p. Another application, carried out by us in a different paper, is a step in the classification of 2-regular reduced projective schemes. Extending a result of Fröberg, we determine which monomial ideals satisfy N2,p. We also apply Green's 'linear syzygy theorem' to deduce a relation between the resolutions of IX and IX∪Γur for a scheme Γ, and apply the result to bound the number of intersection points of certain pairs of varieties such as rational normal scrolls. © Foundation Compositio Mathematica 2005. |
eng |
dc.language.iso |
eng |
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dc.publisher |
Cambridge : Cambridge University Press |
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dc.relation.ispartofseries |
Compositio Mathematica 141 (2005), Nr. 6 |
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dc.rights |
Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich. |
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dc.subject |
Chordal graphs |
eng |
dc.subject |
Linear syzygies |
eng |
dc.subject |
Quadratic ideals |
eng |
dc.subject |
Secants |
eng |
dc.subject.ddc |
510 | Mathematik
|
ger |
dc.title |
Restricting linear syzygies: Algebra and geometry |
eng |
dc.type |
Article |
|
dc.type |
Text |
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dc.relation.issn |
0010-437X |
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dc.relation.doi |
https://doi.org/10.1112/S0010437X05001776 |
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dc.bibliographicCitation.issue |
6 |
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dc.bibliographicCitation.volume |
141 |
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dc.bibliographicCitation.firstPage |
1460 |
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dc.bibliographicCitation.lastPage |
1478 |
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dc.description.version |
publishedVersion |
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tib.accessRights |
frei zug�nglich |
|