Degrees of curves in abelian varieties

Olivier Debarre

Bulletin de la Société Mathématique de France (1994)

  • Volume: 122, Issue: 3, page 343-361
  • ISSN: 0037-9484

How to cite


Debarre, Olivier. "Degrees of curves in abelian varieties." Bulletin de la Société Mathématique de France 122.3 (1994): 343-361. <>.

author = {Debarre, Olivier},
journal = {Bulletin de la Société Mathématique de France},
keywords = {endomorphisms; polarized abelian variety; irreducible curve; Jacobian; geometric genus},
language = {eng},
number = {3},
pages = {343-361},
publisher = {Société mathématique de France},
title = {Degrees of curves in abelian varieties},
url = {},
volume = {122},
year = {1994},

AU - Debarre, Olivier
TI - Degrees of curves in abelian varieties
JO - Bulletin de la Société Mathématique de France
PY - 1994
PB - Société mathématique de France
VL - 122
IS - 3
SP - 343
EP - 361
LA - eng
KW - endomorphisms; polarized abelian variety; irreducible curve; Jacobian; geometric genus
UR -
ER -


  1. [A1] ABRAMOVICH (D.). &#x2014; Subvarieties of Abelian Varieties and of Jacobians of Curves. &#x2014; Ph. D. Thesis, Harvard University, 1991. 
  2. [A2] ABRAMOVICH (D.). &#x2014; Addendum to Curves and Abelian Varieties on Wd(C), unpublished. 
  3. [AH] ABRAMOVICH (D.) and HARRIS (J.). &#x2014; Curves and Abelian Varieties on Wd(C), Comp. Math., t. 78, 1991, p. 227-238. Zbl0748.14010MR92c:14022
  4. [AP] ALZATI (A.) and PIROLA (G.-P.). &#x2014; On Abelian Subvarieties Generated by Symmetric Correspondences, Math. Z., t. 205, 1990, p. 333-342. Zbl0685.14018MR91k:14018
  5. [ACGH] ARBARELLO (E.), CORNALBA (M.), GRIFFITHS (P.) and HARRIS (J.). &#x2014; Geometry Of Algebraic Curves, I, Grundlehren 267, Springer Verlag 1985. Zbl0559.14017MR86h:14019
  6. [B] BALLICO (E.). &#x2014; On Singular Curves in the Case of Positive Characteristic, Math. Nachr., t. 141, 1989, p. 267-273. Zbl0699.14006MR90h:14042
  7. [C] COLLINO (A.). &#x2014; A New Proof of the Ran-Matsusaka Criterion for Jacobians, Proc. Amer. Math. Soc., t. 92, 1984, p. 329-331. Zbl0584.14017MR86a:14026
  8. [D] DEBARRE (O.). &#x2014; Sur les variétés abéliennes dont le diviseur thêta est singulier en codimension 3, Duke Math. J., t. 56, 1988, p. 221-273. Zbl0699.14058MR89f:14047
  9. [DF] DEBARRE (O.) and FAHLAOUI (R.). &#x2014; Abelian Varieties in Wrd(C) and Points of Bounded Degrees On Algebraic Curves, Comp. Math., t. 88, 1993, p. 235-249. Zbl0808.14025MR94h:14028
  10. [Ma] MATSUSAKA (T.). &#x2014; On a Characterization of a Jacobian Variety, Mem. Coll. Sc. Kyoto, Ser. A, t. 23, 1959, p. 1-19. Zbl0094.34103MR21 #7213
  11. [Me] MESTRE (J.-F.). &#x2014; Familles de courbes hyperelliptiques à multiplications réelles, in Arithmetic Algebraic Geometry, Progress in Math. 89, Birkhäuser, 1991. Zbl0754.14020MR92e:14022
  12. [Mi] MILNE (J.). &#x2014; Abelian Varieties, in Arithmetic Geometry, edited by G. Cornell and J. Silverman, Springer Verlag, 1986. Zbl0604.14028MR861974
  13. [M] MORI (S.). &#x2014; The Endomorphism Ring of some Abelian Varieties, Japan J. Math., t. 1, 1976, p. 109-130. Zbl0339.14016MR56 #12013
  14. [Mo] MORIKAWA (H.). &#x2014; Cycles and Endomorphisms of Abelian Varieties, Nagoya Math. J., t. 7, 1954, p. 95-102. Zbl0057.13004MR16,743e
  15. [Mu] MUMFORD (D.). &#x2014; Abelian Varieties. &#x2014; Oxford University Press, 1974. 
  16. [MK] MUMFORD (D.). &#x2014; Varieties Defined by Quadratic Equations, with an appendix by G. Kempf., in Questions On Algebraic Varieties, C.I.M.E., Varenna, 1970. Zbl0198.25801MR44 #209
  17. [R] RAN (Z.). &#x2014; On Subvarieties of Abelian Varieties, Invent. Math., t. 62, 1981, p. 459-479. Zbl0474.14016MR82d:14024
  18. [S] SMYTH (C.). &#x2014; Totally Positive Algebraic Integers of Small Trace, Ann. Inst. Fourier, t. 33, 1984, p. 1-28. Zbl0534.12002MR86f:11091
  19. [TTV] TRAUTZ (W.), TOP (J.) and VERBERKMOES (A.). &#x2014; Explicit Hyperelliptic Curves with Real Multiplication and Permutation Polynomials, Canad. J. Math., t. 43, 1991, p. 1055-1064. Zbl0793.14022MR92j:11058
  20. [vG] VAN DER GEER (G.). &#x2014; Hilbert Modular Surfaces, Ergebnisse der Math. und ihrer Grenz. 16, Springer Verlag, 1988. Zbl0634.14022MR89c:11073
  21. [W] WELTERS (G.). &#x2014; Curves with Twice the Minimal Class on Principally Polarized Abelian Varieties, Proc. Kon. Ned. Akad. van Wetenschappen, Indagationes Math., t. 49, 1987, p. 87-109. Zbl0644.14014MR88c:14061

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.