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- Title
On hypersurfaces containing projective varieties.
- Authors
Euisung Park
- Abstract
Classical Castelnuovo's lemma shows that the number of linearly independent quadratic equations of a nondegenerate irreducible projective variety of codimension c is at most (2c+1)and the equality is attained if and only if the variety is of minimal degree. Also a generalization of Castelnuovo's lemma by G. Fano implies that the next case occurs if and only if the variety is a del Pezzo variety. For curve case, these results are extended to equations of arbitrary degree respectively by J. Harris and S. L'vovsky. This paper is intended to extend these results to arbitrary dimensional varieties and to the next cases.
- Subjects
HYPERSURFACES; VARIETIES (Universal algebra); QUADRATIC equations; GENERALIZATION; MATHEMATICAL analysis
- Publication
Forum Mathematicum, 2015, Vol 27, Issue 2, p843
- ISSN
0933-7741
- Publication type
Article
- DOI
10.1515/forum-2012-0061