Restricting linear syzygies: Algebra and geometry

Show simple item record

dc.identifier.uri Eisenbud, David Green, Mark Hulek, Klaus Popescu, Sorin 2018-01-29T14:34:06Z 2018-01-29T14:34:06Z 2005
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:
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
dc.publisher Cambridge : Cambridge University Press
dc.relation.ispartofseries Compositio Mathematica 141 (2005), Nr. 6
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.
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
dc.type article
dc.type Text
dc.relation.issn 0010-437X
dc.bibliographicCitation.issue 6
dc.bibliographicCitation.volume 141
dc.bibliographicCitation.firstPage 1460
dc.bibliographicCitation.lastPage 1478
dc.description.version publishedVersion
tib.accessRights frei zug�nglich

Files in this item

This item appears in the following Collection(s):

Show simple item record


Search the repository


My Account

Usage Statistics