On the classification of non-normal cubic hypersurfaces

Wanseok Lee; Euisung Park; Peter Schenzel

doi:10.1016/j.jpaa.2010.12.007

On the classification of non-normal cubic hypersurfaces

Wanseok Lee^*
, Euisung Park
, Peter Schenzel

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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
Pages (from-to)	2034-2042
Number of pages	9
Journal	Journal of Pure and Applied Algebra
Volume	215
Issue number	8
DOIs	https://doi.org/10.1016/j.jpaa.2010.12.007
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

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10.1016/j.jpaa.2010.12.007

Cite this

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title = "On the classification of non-normal cubic hypersurfaces",

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.",

author = "Wanseok Lee and Euisung Park and Peter Schenzel",

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.",

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AU - Park, Euisung

AU - Schenzel, Peter

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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.

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DO - 10.1016/j.jpaa.2010.12.007

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SP - 2034

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JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 8

ER -

On the classification of non-normal cubic hypersurfaces

Abstract

Bibliographical note

ASJC Scopus subject areas

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