Some Effects of Veronese Map on Syzygies of Projective Varieties
نویسندگان
چکیده
Let X ⊂ P be a nondegenerate projective variety and let νl : P r → P be the l-th Veronese embedding. In this paper we study the higher normality, defining equations and syzygies among them for the projective embedding νl(X) ⊂ P N . We obtain that for a very ample line bundle L ∈ PicX such that X ⊂ PH(X,L) is m-regular in the sense of Castelnuovo-Mumford, (X,L) satisfies property Nl for all l ≥ m (Theorem 1.5). This is a generalization of M. Green’s work that (P,OPr(l)) satisfies property Nl. Also our result refines works of Ein-Lazarsfeld in [EL], Gallego-Purnaprajna in [GP1] and E. Rubei in [Ru1], [Ru2] and [Ru3].
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