On a linearity criterion for algebraic systems of divisors on a projective variety
Umberto Bartocci; Lucio Guerra
- Volume: 81, Issue: 4, page 347-359
- ISSN: 0392-7881
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topBartocci, Umberto, and Guerra, Lucio. "On a linearity criterion for algebraic systems of divisors on a projective variety." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 81.4 (1987): 347-359. <http://eudml.org/doc/289051>.
@article{Bartocci1987,
abstract = {In the present paper, it is established in any characteristic the validity of a classical theorem of Enriques', stating the linearity of any algebraic system of divisors on a projective variety, which has index 1 and whose generic element is irreducible, as soon as its dimension is at least 2.},
author = {Bartocci, Umberto, Guerra, Lucio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
keywords = {Divisors; Algebraic/linear systems; Chow varieties},
language = {eng},
month = {12},
number = {4},
pages = {347-359},
publisher = {Accademia Nazionale dei Lincei},
title = {On a linearity criterion for algebraic systems of divisors on a projective variety},
url = {http://eudml.org/doc/289051},
volume = {81},
year = {1987},
}
TY - JOUR
AU - Bartocci, Umberto
AU - Guerra, Lucio
TI - On a linearity criterion for algebraic systems of divisors on a projective variety
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1987/12//
PB - Accademia Nazionale dei Lincei
VL - 81
IS - 4
SP - 347
EP - 359
AB - In the present paper, it is established in any characteristic the validity of a classical theorem of Enriques', stating the linearity of any algebraic system of divisors on a projective variety, which has index 1 and whose generic element is irreducible, as soon as its dimension is at least 2.
LA - eng
KW - Divisors; Algebraic/linear systems; Chow varieties
UR - http://eudml.org/doc/289051
ER -
References
top- SEGRE, B. (1972) - Prodromi di Geometria Algebrica, Cremonese, Roma.
- ENRIQUES, F. (1893) - Una questione sulla linearità dei sistemi di curve appartenenti ad una superficie algebrica, «Atti Acc. Naz. Lincei», 2, 3-8. JFM25.1215.01
- ZARISKI, O. (1971) - Algebraic surfaces, 2nd supplemented ed., Springer. Zbl0010.37103MR469915JFM61.0704.01
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- GUERRA, L. (1985) - On Chow varieties of linear systems of divisors on a projective variety, «Rend. Sem. Mat. Univ. Polit. Torino», 43, 457-466. Zbl0626.14005MR884872
- SAMUEL, P. (1967) - Méthodes d'algèbre abstraite en géométrie algébrique, Springer. Zbl0067.38904MR213347
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- SAMUEL, P. (1966) - Lectures on old and new results on algebraic curves, «Tata Inst. Fund. Res.», Bombay. Zbl0165.24102MR222088
- TATE, J.T. (1974) - The arithmetic of Elliptic Curves, «Inventiones Math.», 23, 179-206. Zbl0296.14018MR419359
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