On non-normal del Pezzo varieties

Wanseok Lee; Euisung Park

doi:10.1016/j.jalgebra.2013.04.013

On non-normal del Pezzo varieties

Wanseok Lee, Euisung Park

Department of Mathematics

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

2 Citations (Scopus)

Abstract

Two projective subvarieties of Pr are said to be projectively equivalent if they are identified by a coordinate change. Up to projective equivalence, varieties of minimal degree were completely classified more than one hundred years ago by P. del Pezzo and E. Bertini.As the next case, we study the same problem for del Pezzo varieties, focusing on the non-normal case of degree ≥5. Note that the cases of degrees 3 and 4 were dealt with in Lee et al. (2011) [8] and Lee et al. (2012) [9], respectively. Our main result, Theorem 4.1, provides a complete classification of non-normal del Pezzo varieties of degree at least 5, up to projective equivalence.

Original language	English
Pages (from-to)	11-28
Number of pages	18
Journal	Journal of Algebra
Volume	387
DOIs	https://doi.org/10.1016/j.jalgebra.2013.04.013
Publication status	Published - 2013 Aug 1

Keywords

Del Pezzo variety
Projective equivalence

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2013.04.013

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title = "On non-normal del Pezzo varieties",

abstract = "Two projective subvarieties of Pr are said to be projectively equivalent if they are identified by a coordinate change. Up to projective equivalence, varieties of minimal degree were completely classified more than one hundred years ago by P. del Pezzo and E. Bertini.As the next case, we study the same problem for del Pezzo varieties, focusing on the non-normal case of degree ≥5. Note that the cases of degrees 3 and 4 were dealt with in Lee et al. (2011) [8] and Lee et al. (2012) [9], respectively. Our main result, Theorem 4.1, provides a complete classification of non-normal del Pezzo varieties of degree at least 5, up to projective equivalence.",

keywords = "Del Pezzo variety, Projective equivalence",

author = "Wanseok Lee and Euisung Park",

note = "Funding Information: The first named author was supported by the National Researcher program 2010-0020413 of NRF and MEST. The second named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0007329). The authors would like to thank Professors Atsushi Noma for stimulating comments for Theorem 4.5. The authors also thank the referee for a careful study of the manuscript and the suggested improvements.",

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doi = "10.1016/j.jalgebra.2013.04.013",

language = "English",

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journal = "Journal of Algebra",

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AU - Lee, Wanseok

AU - Park, Euisung

N1 - Funding Information: The first named author was supported by the National Researcher program 2010-0020413 of NRF and MEST. The second named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0007329). The authors would like to thank Professors Atsushi Noma for stimulating comments for Theorem 4.5. The authors also thank the referee for a careful study of the manuscript and the suggested improvements.

PY - 2013/8/1

Y1 - 2013/8/1

N2 - Two projective subvarieties of Pr are said to be projectively equivalent if they are identified by a coordinate change. Up to projective equivalence, varieties of minimal degree were completely classified more than one hundred years ago by P. del Pezzo and E. Bertini.As the next case, we study the same problem for del Pezzo varieties, focusing on the non-normal case of degree ≥5. Note that the cases of degrees 3 and 4 were dealt with in Lee et al. (2011) [8] and Lee et al. (2012) [9], respectively. Our main result, Theorem 4.1, provides a complete classification of non-normal del Pezzo varieties of degree at least 5, up to projective equivalence.

AB - Two projective subvarieties of Pr are said to be projectively equivalent if they are identified by a coordinate change. Up to projective equivalence, varieties of minimal degree were completely classified more than one hundred years ago by P. del Pezzo and E. Bertini.As the next case, we study the same problem for del Pezzo varieties, focusing on the non-normal case of degree ≥5. Note that the cases of degrees 3 and 4 were dealt with in Lee et al. (2011) [8] and Lee et al. (2012) [9], respectively. Our main result, Theorem 4.1, provides a complete classification of non-normal del Pezzo varieties of degree at least 5, up to projective equivalence.

KW - Del Pezzo variety

KW - Projective equivalence

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DO - 10.1016/j.jalgebra.2013.04.013

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VL - 387

SP - 11

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

On non-normal del Pezzo varieties

Abstract

Keywords

ASJC Scopus subject areas

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