Some Effects of Veronese Map on Syzygies of Projective Varieties

Abstract

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… (More)

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