Rational connectivity and sections of families over curves
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 5, pp. 671-692.
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     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},
     pages = {671--692},
     publisher = {Elsevier},
     volume = {Ser. 4, 38},
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     doi = {10.1016/j.ansens.2005.07.003},
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     zbl = {1092.14062},
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     url = {http://archive.numdam.org/articles/10.1016/j.ansens.2005.07.003/}
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Graber, Tom; Harris, Joe; Mazur, Barry; Starr, Jason. Rational connectivity and sections of families over curves. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 5, pp. 671-692. doi : 10.1016/j.ansens.2005.07.003. http://archive.numdam.org/articles/10.1016/j.ansens.2005.07.003/

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

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

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

[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

[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 | Zbl

[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 | Zbl

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

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

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

[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 | Zbl

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

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

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

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

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

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

[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.

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