TY - JOUR

T1 - On the classification of non-normal cubic hypersurfaces

AU - Lee, Wanseok

AU - Park, Euisung

AU - Schenzel, Peter

N1 - 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.

PY - 2011/8

Y1 - 2011/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79952486445&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2010.12.007

DO - 10.1016/j.jpaa.2010.12.007

M3 - Article

AN - SCOPUS:79952486445

VL - 215

SP - 2034

EP - 2042

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 8

ER -