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On quasi-complete intersections of codimension

Authors:	Youngook Choi

Institution:	Department of Mathematics, Korea Advanced Institute of Science and Technology, 373-1 Gusung-dong Yusung-gu, Daejeon, Korea

Abstract:	In this paper, we prove that if $X\subset\mathbb{P}^n$ , $n\ge 4$ , is a locally complete intersection of pure codimension and defined scheme-theoretically by three hypersurfaces of degrees $d_1\ge d_2\ge d_3$ , then $H^1(\mathbb{P}^n,\mathcal{I}_X(j))=0$ for using liaison theory and the Arapura vanishing theorem for singular varieties. As a corollary, a smooth threefold $X\subset\mathbb{P}^5$ is projectively normal if is defined by three quintic hypersurfaces.

Keywords:	Quasi-complete intersections liaison normality defining equations

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