We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
On hyperquadrics containing projective varieties.
- Authors
Park, Euisung
- Abstract
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 + 1 2) {{{c+1}\choose{2}}} 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 + 1 2) - 3 {{{c+1}\choose{2}}-3} linearly independent quadratic equations. Also we investigate the zero set of those quadratic equations and apply our results to projective varieties of degree ≥ 2 c + 1 {\geq 2c+1}.
- Subjects
MATHEMATICS; GENERALIZATION
- Publication
Forum Mathematicum, 2020, Vol 32, Issue 5, p1199
- ISSN
0933-7741
- Publication type
Article
- DOI
10.1515/forum-2019-0275