Rational connectivity and sections of families over curves
Graber, Tom ; Harris, Joe ; Mazur, Barry ; Starr, Jason
Annales scientifiques de l'École Normale Supérieure, Tome 38 (2005), p. 671-692 / Harvested from Numdam
@article{ASENS_2005_4_38_5_671_0,
     author = {Graber, Tom and Harris, Joe and Mazur, Barry and Starr, Jason},
     title = {Rational connectivity and sections of families over curves},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {38},
     year = {2005},
     pages = {671-692},
     doi = {10.1016/j.ansens.2005.07.003},
     mrnumber = {2195256},
     zbl = {1092.14062},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_2005_4_38_5_671_0}
}
Graber, Tom; Harris, Joe; Mazur, Barry; Starr, Jason. Rational connectivity and sections of families over curves. Annales scientifiques de l'École Normale Supérieure, Tome 38 (2005) pp. 671-692. doi : 10.1016/j.ansens.2005.07.003. http://gdmltest.u-ga.fr/item/ASENS_2005_4_38_5_671_0/

[1] Campana F., Connexité rationnelle des variétés de Fano, Ann. Sci. École. Norm. Sup. 25 (1992) 539-545. | Numdam | MR 1191735 | Zbl 0783.14022

[2] Clemens H., Curves on generic hypersurfaces, Ann. Sci. École Norm. Sup. (4) 19 (1986) 629-636. | Numdam | MR 875091 | Zbl 0611.14024

[3] Debarre O., Higher-Dimensional Algebraic Geometry, Universitext, Springer, Berlin, 2001. | MR 1841091 | Zbl 0978.14001

[4] Fulton W., Pandharipande R., Notes on stable maps and quantum cohomology, in: Algebraic Geometry-Santa Cruz 1995, American Mathematical Society, Providence, RI, 1997, pp. 45-96. | Zbl 0898.14018

[5] Graber T., Harris J., Mazur B., Starr J., Arithmetic questions related to rationally connected varieties, in: The Legacy of Niels Henrik Abel: The Abel Bicentennial, Oslo 2002, Springer, Berlin, 2004, pp. 531-543. | MR 2077583 | Zbl 1071.14053

[6] Graber T., Harris J., Mazur B., Starr J., Jumps in Mordell-Weil rank and arithmetic surjectivity, in: Arithmetic of Higher-Dimensional Algebraic Varieties, Palo Alto, CA 2002, Birkhäuser, Basel, 2004, pp. 141-147. | MR 2029867 | Zbl 1075.14021

[7] Graber T., Harris J., Starr J., Families of rationally connected varieties, J. Amer. Math. Soc. 16 (2003) 57-67. | MR 1937199 | Zbl 1092.14063

[8] Grothendieck A., Serre J.-P., Colmez P., Serre J.-P. (Eds.), Correspondance Grothendieck-Serre, Société Math. de France, Paris, 2001. | MR 1942134 | Zbl 0986.01019

[9] Goresky M., Macpherson R., Stratified Morse Theory, Ergeb. Math., vol. 14, Springer, Berlin, 1988. | MR 932724 | Zbl 0639.14012

[10] Hamm H., Lefschetz theorems for singular varieties, in: Singularities, Part 1, Arcata, CA 1981, Proc. Sympos. Pure Math., vol. 40, American Mathematical Society, Providence, RI, 1983, pp. 547-557. | MR 713091 | Zbl 0525.14011

[11] Hartshorne R., Algebraic Geometry, Graduate Texts in Math., vol. 52, Springer, Berlin, 1977. | MR 463157 | Zbl 0367.14001

[12] Kollár J., Rational Curves on Algebraic Varieties, Ergeb. Math., vol. 32, Springer, Berlin, 1996. | MR 1440180 | Zbl 0877.14012

[13] Kollár J., Miyaoka Y., Mori S., Rationally connected varieties, J. Algebraic Geom. 1 (1992) 429-448. | MR 1158625 | Zbl 0780.14026

[14] Lafon G., Une surface d’Enriques sans point sur Ct, C. R. Math. Acad. Sci. Paris 338 (2004) 51-54. | MR 2038084 | Zbl 1040.14020

[15] Mori S., Projective manifolds with ample tangent bundles, Ann. of Math. 110 (1979) 593-606. | MR 554387 | Zbl 0423.14006

[16] Mumford D., Abelian Varieties, Oxford University Press, Oxford, 1970. | MR 282985 | Zbl 0223.14022

[17] Starr J., Explicit computations related to Rational connectivity … by Graber, Harris, Mazur, and Starr, available at, http://www-math.mit.edu/~jstarr/papers/explicit2.pdf.