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G. Castelnuovo (1893)
Sui multipli di una serie lineare di gruppi di punti appartenente ad una curva algebricaRendiconti del Circolo Matematico di Palermo, 7
- Publisher
- de Gruyter
- Copyright
- Copyright © 2015 by the
- ISSN
- 0933-7741
- eISSN
- 1435-5337
- DOI
- 10.1515/forum-2012-0061
- Publisher site
- See Article on Publisher Site
Abstract
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 c + 1 2 ${{\binom{c+1}{2}}}$ 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.
Journal
Forum Mathematicum – de Gruyter
Published: Mar 1, 2015