Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 

 

Families of rationally connected varieties


Authors: Tom Graber, Joe Harris and Jason Starr
Journal: J. Amer. Math. Soc. 16 (2003), 57-67
MSC (2000): Primary 14M20, 14D05
Published electronically: July 29, 2002
MathSciNet review: 1937199
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that every one-parameter family of complex rationally connected varieties has a section.


References [Enhancements On Off] (What's this?)

  • [B] K. Behrend, Gromov-Witten invariants in algebraic geometry, Invent. Math. 127 (1997), no. 3, 601–617. MR 1431140, 10.1007/s002220050132
  • [BF] K. Behrend and B. Fantechi, The intrinsic normal cone, Invent. Math. 128 (1997), no. 1, 45–88. MR 1437495, 10.1007/s002220050136
  • [BM] K. Behrend and Yu. Manin, Stacks of stable maps and Gromov-Witten invariants, Duke Math. J. 85 (1996), no. 1, 1–60. MR 1412436, 10.1215/S0012-7094-96-08501-4
  • [Ca] F. Campana, Connexité rationnelle des variétés de Fano, Ann. Sci. École Norm. Sup. (4) 25 (1992), no. 5, 539–545 (French). MR 1191735
  • [C] A. Clebsch, Zur Theorie der Riemann'schen Flachen, Math Ann. 6 (1872), 216-230 Springer-Verlag, Berlin, 1996.
  • [FaP] B. Fantechi, R. Pandharipande, Stable maps and branch divisors, Compositio Math. 130 (2002), 345-364.
  • [F] William Fulton, Hurwitz schemes and irreducibility of moduli of algebraic curves, Ann. of Math. (2) 90 (1969), 542–575. MR 0260752
  • [FP] W. Fulton and R. Pandharipande, Notes on stable maps and quantum cohomology, Algebraic geometry—Santa Cruz 1995, Proc. Sympos. Pure Math., vol. 62, Amer. Math. Soc., Providence, RI, 1997, pp. 45–96. MR 1492534, 10.1090/pspum/062.2/1492534
  • [GHS] T. Graber, J. Harris, J. Starr, A note on Hurwitz schemes of covers of a positive genus curve, preprint alg-geom/0205056.
  • [H] A. Hurwitz, Ueber Riemann'sche Flächen mit gegebenen Verzweigungspunkten, Math. Ann. 39 (1891) 1-61.
  • [K] János Kollár, Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 32, Springer-Verlag, Berlin, 1996. MR 1440180
  • [KMM] János Kollár, Yoichi Miyaoka, and Shigefumi Mori, Rationally connected varieties, J. Algebraic Geom. 1 (1992), no. 3, 429–448. MR 1158625

Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 14M20, 14D05

Retrieve articles in all journals with MSC (2000): 14M20, 14D05


Additional Information

Tom Graber
Affiliation: Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, Massachusetts 02138
Email: graber@math.harvard.edu

Joe Harris
Affiliation: Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, Massachusetts 02138
Email: harris@math.harvard.edu

Jason Starr
Affiliation: Department of Mathmatics, Massachusetts Institute of technology, Cambridge, Massachusetts 02139
Email: jstarr@math.mit.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-02-00402-2
Received by editor(s): September 6, 2001
Received by editor(s) in revised form: May 3, 2002
Published electronically: July 29, 2002
Additional Notes: The first author was partially supported by an NSF Postdoctoral Fellowship.
The second author was partially supported by NSF grant DMS9900025.
The third author was partially supported by a Sloan Dissertation Fellowship.
Article copyright: © Copyright 2002 American Mathematical Society