Rational connectivity and sections of families over curves

Tom Graber; Joe Harris; Barry Mazur; Jason Starr

Annales scientifiques de l'École Normale Supérieure (2005)

  • Volume: 38, Issue: 5, page 671-692
  • ISSN: 0012-9593

How to cite


Graber, Tom, et al. "Rational connectivity and sections of families over curves." Annales scientifiques de l'École Normale Supérieure 38.5 (2005): 671-692. <http://eudml.org/doc/82671>.

author = {Graber, Tom, Harris, Joe, Mazur, Barry, Starr, Jason},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {rationally connected; stable map; triangle},
language = {eng},
number = {5},
pages = {671-692},
publisher = {Elsevier},
title = {Rational connectivity and sections of families over curves},
url = {http://eudml.org/doc/82671},
volume = {38},
year = {2005},

AU - Graber, Tom
AU - Harris, Joe
AU - Mazur, Barry
AU - Starr, Jason
TI - Rational connectivity and sections of families over curves
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2005
PB - Elsevier
VL - 38
IS - 5
SP - 671
EP - 692
LA - eng
KW - rationally connected; stable map; triangle
UR - http://eudml.org/doc/82671
ER -


  1. [1] Campana F., Connexité rationnelle des variétés de Fano, Ann. Sci. École. Norm. Sup.25 (1992) 539-545. Zbl0783.14022MR1191735
  2. [2] Clemens H., Curves on generic hypersurfaces, Ann. Sci. École Norm. Sup. (4)19 (1986) 629-636. Zbl0611.14024MR875091
  3. [3] Debarre O., Higher-Dimensional Algebraic Geometry, Universitext, Springer, Berlin, 2001. Zbl0978.14001MR1841091
  4. [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. Zbl0898.14018
  5. [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. Zbl1071.14053MR2077583
  6. [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. Zbl1075.14021MR2029867
  7. [7] Graber T., Harris J., Starr J., Families of rationally connected varieties, J. Amer. Math. Soc.16 (2003) 57-67. Zbl1092.14063MR1937199
  8. [8] Grothendieck A., Serre J.-P., Colmez P., Serre J.-P. (Eds.), Correspondance Grothendieck-Serre, Société Math. de France, Paris, 2001. Zbl0986.01019MR1942134
  9. [9] Goresky M., MacPherson R., Stratified Morse Theory, Ergeb. Math., vol. 14, Springer, Berlin, 1988. Zbl0639.14012MR932724
  10. [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. Zbl0525.14011MR713091
  11. [11] Hartshorne R., Algebraic Geometry, Graduate Texts in Math., vol. 52, Springer, Berlin, 1977. Zbl0367.14001MR463157
  12. [12] Kollár J., Rational Curves on Algebraic Varieties, Ergeb. Math., vol. 32, Springer, Berlin, 1996. Zbl0877.14012MR1440180
  13. [13] Kollár J., Miyaoka Y., Mori S., Rationally connected varieties, J. Algebraic Geom.1 (1992) 429-448. Zbl0780.14026MR1158625
  14. [14] Lafon G., Une surface d’Enriques sans point sur C t , C. R. Math. Acad. Sci. Paris338 (2004) 51-54. Zbl1040.14020MR2038084
  15. [15] Mori S., Projective manifolds with ample tangent bundles, Ann. of Math.110 (1979) 593-606. Zbl0423.14006MR554387
  16. [16] Mumford D., Abelian Varieties, Oxford University Press, Oxford, 1970. Zbl0223.14022MR282985
  17. [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. 

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.