Abstract
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 language | English |
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Pages (from-to) | 2034-2042 |
Number of pages | 9 |
Journal | Journal of Pure and Applied Algebra |
Volume | 215 |
Issue number | 8 |
DOIs | |
Publication status | Published - 2011 Aug |
Bibliographical note
Funding Information:The first named author was supported by the SRC program of Korea Science and Engineering Foundation (KOSEF) grant funded by the Korean government (MEST) (No. R11-2007-035-02001-0). The second named author was supported by Mid-career Researcher Program through NRF grant funded by the MEST(No. R01-2008-0061792). The third named author is grateful to KAIST and KIAS for supporting this research. The authors also thank the referee for a careful study of the manuscript and the suggested improvements.
ASJC Scopus subject areas
- Algebra and Number Theory