On the classification of non-normal cubic hypersurfaces

Wanseok Lee, Euisung Park, Peter Schenzel

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


In this article we study the classification of non-normal cubic hypersurfaces over an algebraically closed field K of arbitrary characteristic. Let X⊂PKr 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 X⊂PKr for r≤4. We prove that there are precisely five non-normal cubic equations (resp. six non-normal cubic equations) when charK≠2,3 (resp. when charK is either 2 or 3), up to projective equivalence. Also we describe the normalization of X in detail.

Original languageEnglish
Pages (from-to)2034-2042
Number of pages9
JournalJournal of Pure and Applied Algebra
Issue number8
Publication statusPublished - 2011 Aug

ASJC Scopus subject areas

  • Algebra and Number Theory


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