Geodesic
Logarithmic Gromov-Witten invariants
Gross, Mark1 ; Siebert, Bernd2
1 Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112
2 FB Mathematik, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany
Journal of the American Mathematical Society, Tome 26 (2013) no. 2, pp. 451-510

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S0894-0347-2012-00757-7

Gross, Mark 1 ; Siebert, Bernd 2

1 Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112
2 FB Mathematik, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany 
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Gross, Mark; Siebert, Bernd. Logarithmic Gromov-Witten invariants. Journal of the American Mathematical Society, Tome 26 (2013) no. 2, pp. 451-510. doi: 10.1090/S0894-0347-2012-00757-7

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