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dc.contributor.author Han, Kang Jin ko
dc.contributor.author Kwak, Sijong ko
dc.date.available 2018-02-05T04:13:20Z -
dc.date.created 2018-01-17 -
dc.date.issued 2015-02 -
dc.identifier.citation Mathematische Annalen, v.361, no.1-2, pp.535 - 561 -
dc.identifier.issn 0025-5831 -
dc.identifier.uri http://hdl.handle.net/20.500.11750/5677 -
dc.description.abstract In the present paper, we consider upper bounds of higher linear syzygies i.e. graded Betti numbers in the first linear strand of the minimal free resolutions of projective varieties in arbitrary characteristic. For this purpose, we first remind ‘Partial Elimination Ideals (PEIs)’ theory and introduce a new framework in which one can study the syzygies of embedded projective varieties well using PEIs theory and the reduction method via inner projections. Next we establish fundamental inequalities which govern the relations between the graded Betti numbers in the first linear strand of an algebraic set X and those of its inner projection Xq. Using these results, we obtain some natural sharp upper bounds for higher linear syzygies of any nondegenerate projective variety in terms of the codimension with respect to its own embedding and classify what the extremal case and the next-to-extremal case are. This is a generalization of Castelnuovo and Fano’s results on the number of quadrics containing a given variety and another characterization of varieties of minimal degree and del Pezzo varieties from the viewpoint of ‘syzygies’. Note that our method could also be applied to get similar results for more general categories (e.g. connected in codimension one algebraic sets). © 2014, Springer-Verlag Berlin Heidelberg. -
dc.language English -
dc.publisher SPRINGER HEIDELBERG -
dc.subject GENERIC INITIAL IDEALS -
dc.subject DEGREE-COMPLEXITY -
dc.subject MINIMAL DEGREE -
dc.subject GEOMETRY -
dc.subject POINTS -
dc.subject CURVES -
dc.title Sharp bounds for higher linear syzygies and classifications of projective varieties -
dc.type Article -
dc.identifier.doi 10.1007/s00208-014-1084-9 -
dc.identifier.wosid 000348306200020 -
dc.identifier.scopusid 2-s2.0-84938203812 -
dc.type.local Article(Overseas) -
dc.type.rims ART -
dc.description.journalClass 1 -
dc.contributor.nonIdAuthor Kwak, Sijong -
dc.identifier.citationVolume 361 -
dc.identifier.citationNumber 1-2 -
dc.identifier.citationStartPage 535 -
dc.identifier.citationEndPage 561 -
dc.identifier.citationTitle Mathematische Annalen -
dc.type.journalArticle Article -
dc.description.isOpenAccess N -
dc.contributor.affiliatedAuthor Han, Kang Jin -
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