Curves of minimal genus on a general abelian variety

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1. [ACGH] E. Arbarello, M. Comalba, P. Griffiths and J. Harris, Geometry of algebraic curves. I, Grundlehren der Math.267, Springer-Verlag, 1984. Zbl0559.14017
2. [AP] A. Alzati and P. Pirola, On abelian subvarieties generated by symmetric correspondences, Math. Z.205 (1990), 333-342. Zbl0685.14018MR1082859
3. [Ba] F. Bardelli, Curves of genus three on a general abelian threefold and the non finite generation of the Griffiths group, in Arithmetic of Complex Manifolds, Proceedings, Erlangen, 1988, ed. W. Barth, H. Lange, Springer Lecture Notes in Math., 1399 (1989), 10-26. Zbl0703.14004MR1034253
4. [B] A. Beauville, Prym varieties and the Schottky problem, Invent. Math.41 (1977), 149-196. Zbl0333.14013MR572974
5. [BL] Ch. Birkenhake and H. Lange, Complex abelian varieties, Grundlehren der math. Wiss., Springer-Verlag, 1992. Zbl0779.14012MR1217487
6. [C] C. Ciliberto, Alcune applicazioni di un classico procedimento di Castelnuovo, Sem. di variabili Complesse, Univ. di Bologna, 1982-83,17-43. Zbl0612.14028
7. [CC] L. Chiantini and C. Ciliberto, A few remarks on the lifting problem, preprint (1992). MR1265310
8. [CGT] C. Ciliberto, G. van der Geer and M. Teixidor, On the number of parameters of curves whose Jacobians possess nontrivial endomorphisms, J. Alg. Geom.1 (1992), 215-229. Zbl0806.14020MR1144437
9. [CG] C. Ciliberto and G. van der Geer, Subvarieties of the moduli space of curves parametrizing Jacobians with non-trivial endomorphisms, Am. J. Math.114 (1991), 551-570. Zbl0766.14016MR1165353
10. [Cl] H. Clemens, Double solids, Adv. in Math.47 (1983). Zbl0509.14045MR690465
11. [D] R. Donagi, The tetragonal construction, Bull. Amer. Math. Soc.4 (1981), 181-185. Zbl0491.14016MR598683
12. [De] O. Debarre, Degree of curves in abelian varieties, preprint (1992). MR1294460
13. [DS] R. Donagi and R. Smith, The structure of the Prym map, Acta Math.146 (1981), 25-102. Zbl0538.14019MR594627
14. [G] Ph. Griffiths, Periods of integrals over algebraic manifolds, III, Publ. Math. IHES, 38 (1970), 125-180. Zbl0212.53503MR282990
15. [K 1] V. Kanev, Theta divisors of generalized Prym varieties I, Springer Lecture Notes in Math. 1124 (1985), 166-215. Zbl0575.14037MR805335
16. [K 2] V. Kanev, Principal polarizations of Prym-Tjurin varieties, preprint ( ). Zbl0694.14009
17. [M] D. Mumford, Prym varieties I, Contribution to Analysis, Academic Press, 1974. Zbl0299.14018MR379510
18. [P] G.P. Pirola, Abel-Jacobi invariant and curves on generic abelian varieties, preprint (1992). Zbl0837.14036MR1336610
19. [R] S. Recillas, Jacobian of curves with a g1 4 are Prym varieties of trigonal curves, Bol. Soc. Mat. Mexicana, 19 (1974), 9-13. Zbl0343.14012MR480505
20. [S] F. Severi, Sulle corrispondenze fra i punti di una curva algebrica e sopra certe classi di superficie, Mem. Accad. Sci.Torino, (2) 54 (1903). Zbl35.0629.01JFM35.0629.01
21. [Se] E. Sernesi, Neutral linear series, preprint, Erlangen (1988). 
22. [T] R. Torelli, Sulle serie algebriche semplicemente infinite di gruppi di punti appartenenti a una curva algebrica, Rend. Circ. Mat.Palermo, 37 (1914). Zbl45.0816.02JFM45.0816.02
23. [W] G. Welters, Curves of twice the minimal class on principally polarized abelian varieties, Indagationes Math.49 (1987), 87-109. Zbl0644.14014MR883371