On a linearity criterion for algebraic systems of divisors on a projective variety

Umberto Bartocci; Lucio Guerra

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1987)

  • Volume: 81, Issue: 4, page 347-359
  • ISSN: 1120-6330

Abstract

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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.

How to cite

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Bartocci, 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 Lincei. Matematica e Applicazioni 81.4 (1987): 347-359. <http://eudml.org/doc/287226>.

@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 Lincei. Matematica e Applicazioni},
keywords = {Divisors; Algebraic/linear systems; Chow varieties; linearity criterion for algebraic systems of divisors; index 1; least 2},
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/287226},
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 Lincei. Matematica e Applicazioni
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; linearity criterion for algebraic systems of divisors; index 1; least 2
UR - http://eudml.org/doc/287226
ER -

References

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  1. SEGRE, B. (1972) - Prodromi di Geometria Algebrica, Cremonese, Roma. Zbl0281.14001
  2. ENRIQUES, F. (1893) - Una questione sulla linearità dei sistemi di curve appartenenti ad una superficie algebrica, «Atti Acc. Naz. Lincei», 2, 3-8. Zbl25.1215.01JFM25.1215.01
  3. ZARISKI, O. (1971) - Algebraic surfaces, 2nd supplemented ed., Springer. Zbl0010.37103MR469915JFM61.0704.01
  4. BARTOCCI, U. (1973) - On a classical theorem concerning algebraic systems of hypersurfaces in a projective space or in a projective variety, «Atti Acc. Naz. Lincei», 55, 364-376. Zbl0302.14013MR569682
  5. CHOW, W.L. and VAN DER WAERDEN, B.L. (1937) - Zur algebraischen Geometrie IX, «Math. Ann.», 113, 692-704. Zbl0016.04004MR1513117JFM62.0772.02
  6. 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
  7. SAMUEL, P. (1967) - Méthodes d'algèbre abstraite en géométrie algébrique, Springer. Zbl0067.38904MR213347
  8. WEIL, A. (1954) - Sur les critères d'équivalence en géométrie algébrique, «Math. Ann.», 128, 95-127. Zbl0057.13002MR65219
  9. SEIDENBERG, A. (1950) - The hyperplane sections of normal varieties, «Trans. A.M.S.», 69, 357-386. Zbl0040.23501MR37548
  10. SAMUEL, P. (1966) - Lectures on old and new results on algebraic curves, «Tata Inst. Fund. Res.», Bombay. Zbl0165.24102MR222088
  11. TATE, J.T. (1974) - The arithmetic of Elliptic Curves, «Inventiones Math.», 23, 179-206. Zbl0296.14018MR419359

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