On hyperquadrics containing projective varieties

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Classical Castelnuovo Lemma shows that the number of linearly independent quadratic equations of a nondegenerate irreducible projective variety of codimension c is at most (c+12) and the equality is attained if and only if the variety is of minimal degree. Also G. Fano's generalization of Castelnuovo Lemma implies that the next case occurs if and only if the variety is a del Pezzo variety. Recently, these results are extended to the next case in [E. Park, On hypersurfaces containing projective varieties, Forum Math. 27 2015, 2, 843-875]. This paper is intended to complete the classification of varieties satisfying at least (c+12) - 3 linearly independent quadratic equations. Also we investigate the zero set of those quadratic equations and apply our results to projective varieties of degree ≥ 2c+1.

Original languageEnglish
Pages (from-to)1199-1209
Number of pages11
JournalForum Mathematicum
Issue number5
Publication statusPublished - 2020 Sept 1


  • Castelnuovo theory
  • Quadratic equations
  • projective varieties of low degree

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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