Geodesic
Toric Degenerations, Tropical Curve, and Gromov–Witten Invariants of Fano Manifolds
Canadian journal of mathematics, Tome 67 (2015) no. 3, pp. 667-695

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DOI

In this paper, we give a tropical method for computing Gromov–Witten type invariants of Fano manifolds of special type. This method applies to those Fano manifolds that admit toric degenerations to toric Fano varieties with singularities allowing small resolutions. Examples include (generalized) flag manifolds of type $\text{A}$ and some moduli space of rank two bundles on a genus two curve.
DOI : 10.4153/CJM-2014-006-3
Mots-clés : 14J45, Fano varieties, Gromov–Witten invariants, tropical curves 
Nishinou, Takeo. Toric Degenerations, Tropical Curve, and Gromov–Witten Invariants of Fano Manifolds. Canadian journal of mathematics, Tome 67 (2015) no. 3, pp. 667-695. doi: 10.4153/CJM-2014-006-3
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     title = {Toric {Degenerations,} {Tropical} {Curve,} and {Gromov{\textendash}Witten} {Invariants} of {Fano} {Manifolds}},
     journal = {Canadian journal of mathematics},
     pages = {667--695},
     year = {2015},
     volume = {67},
     number = {3},
     doi = {10.4153/CJM-2014-006-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2014-006-3/}
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