On the classification of non-normal cubic hypersurfaces
- Authors
- Lee, Wanseok; Park, Euisung; Schenzel, Peter
- Issue Date
- 8월-2011
- Publisher
- ELSEVIER SCIENCE BV
- Citation
- JOURNAL OF PURE AND APPLIED ALGEBRA, v.215, no.8, pp.2034 - 2042
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF PURE AND APPLIED ALGEBRA
- Volume
- 215
- Number
- 8
- Start Page
- 2034
- End Page
- 2042
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/111870
- DOI
- 10.1016/j.jpaa.2010.12.007
- ISSN
- 0022-4049
- Abstract
- In this article we study the classification of non-normal cubic hypersurfaces over an algebraically closed field K of arbitrary characteristic. Let X subset of P-K(r), 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 subset of P-K(r) for r <= 4. We prove that there are precisely five non-normal cubic equations (resp. six non-normal cubic equations) when char K not equal 2, 3 (resp. when char K is either 2 or 3), up to projective equivalence. Also we describe the normalization of X in detail. (C) 2011 Elsevier B.V. All rights reserved.
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