On the classification of non-normal cubic hypersurfaces |
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| Authors: | Wanseok Lee Euisung Park |
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| Institution: | a School of Mathematics, Korea Institute for Advanced Study, 207-43 Cheongryangri-dong, Dongdaemun-gu, Seoul 130-722, Republic of Koreab Department of Mathematics, Korea University, Seoul 136-701, Republic of Koreac Martin-Luther-Universität Halle-Wittenberg, Institut für Informatik, Von-Seckendorff-Platz 1, D-06120 Halle (Saale), Germany |
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| Abstract: | In this article we study the classification of non-normal cubic hypersurfaces over an algebraically closed field K of arbitrary characteristic. Let  be an irreducible non-normal cubic hypersurface. If r≥5, then X is necessarily a cone (Remark 2.3). In view of this fact it suffices to classify irreducible non-normal cubic hypersurfaces  for r≤4. We prove that there are precisely five non-normal cubic equations (resp. six non-normal cubic equations) when  (resp. when  is either 2 or 3), up to projective equivalence. Also we describe the normalization of X in detail. |
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| Keywords: | Primary 14N15 Secondary 51N35 |
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