On non-normal del Pezzo varieties

Wanseok Lee, Euisung Park

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)11-28
Number of pages18
JournalJournal of Algebra
Volume387
DOIs
Publication statusPublished - 2013 Aug 1

Bibliographical 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.

Keywords

  • Del Pezzo variety
  • Projective equivalence

ASJC Scopus subject areas

  • Algebra and Number Theory

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