Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Families of rationally connected varieties
HTML articles powered by AMS MathViewer

by Tom Graber, Joe Harris and Jason Starr HTML | PDF
J. Amer. Math. Soc. 16 (2003), 57-67 Request permission

Abstract:

We prove that every one-parameter family of complex rationally connected varieties has a section.
References
  • K. Behrend, Gromov-Witten invariants in algebraic geometry, Invent. Math. 127 (1997), no. 3, 601–617. MR 1431140, DOI 10.1007/s002220050132
  • K. Behrend and B. Fantechi, The intrinsic normal cone, Invent. Math. 128 (1997), no. 1, 45–88. MR 1437495, DOI 10.1007/s002220050136
  • K. Behrend and Yu. Manin, Stacks of stable maps and Gromov-Witten invariants, Duke Math. J. 85 (1996), no. 1, 1–60. MR 1412436, DOI 10.1215/S0012-7094-96-08501-4
  • F. Campana, Connexité rationnelle des variétés de Fano, Ann. Sci. École Norm. Sup. (4) 25 (1992), no. 5, 539–545 (French). MR 1191735, DOI 10.24033/asens.1658
  • [C]C A. Clebsch, Zur Theorie der Riemann’schen Flachen, Math Ann. 6 (1872), 216-230 Springer-Verlag, Berlin, 1996. [FaP]FaP B. Fantechi, R. Pandharipande, Stable maps and branch divisors, Compositio Math. 130 (2002), 345-364.
  • William Fulton, Hurwitz schemes and irreducibility of moduli of algebraic curves, Ann. of Math. (2) 90 (1969), 542–575. MR 260752, DOI 10.2307/1970748
  • 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, DOI 10.1090/pspum/062.2/1492534
  • [GHS]GHS2 T. Graber, J. Harris, J. Starr, A note on Hurwitz schemes of covers of a positive genus curve, preprint alg-geom/0205056. [H]H A. Hurwitz, Ueber Riemann’sche Flächen mit gegebenen Verzweigungspunkten, Math. Ann. 39 (1891) 1-61.
  • 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, DOI 10.1007/978-3-662-03276-3
  • 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
  • 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.
  • © Copyright 2002 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 16 (2003), 57-67
  • MSC (2000): Primary 14M20, 14D05
  • DOI: https://doi.org/10.1090/S0894-0347-02-00402-2
  • MathSciNet review: 1937199