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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 mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Logarithmic Gromov-Witten invariants
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by Mark Gross and Bernd Siebert
J. Amer. Math. Soc. 26 (2013), 451-510
Published electronically: November 20, 2012


The goal of this paper is to give a general theory of logarithmic Gromov-Witten invariants. This gives a vast generalization of the theory of relative Gromov-Witten invariants introduced by Li-Ruan, Ionel-Parker, and Jun Li and completes a program first proposed by the second named author in 2002. One considers target spaces $X$ carrying a log structure. Domains of stable log curves are log smooth curves. Algebraicity of the stack of such stable log maps is proven, subject only to the hypothesis that the log structure on $X$ is fine, saturated, and Zariski. A notion of basic stable log map is introduced; all stable log maps are pull-backs of basic stable log maps via base-change. With certain additional hypotheses, the stack of basic stable log maps is proven to be proper. Under these hypotheses and the additional hypothesis that $X$ is log smooth, one obtains a theory of log Gromov-Witten invariants.
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Bibliographic Information
  • Mark Gross
  • Affiliation: Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112
  • MR Author ID: 308804
  • Email:
  • Bernd Siebert
  • Affiliation: FB Mathematik, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany
  • Email:
  • Received by editor(s): March 16, 2011
  • Received by editor(s) in revised form: August 26, 2011, and July 30, 2012
  • Published electronically: November 20, 2012
  • Additional Notes: This work was partially supported by NSF grants 0505325 and 0805328.
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 26 (2013), 451-510
  • MSC (2010): Primary 14D20, 14N35
  • DOI:
  • MathSciNet review: 3011419