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Toric Degenerations, Tropical Curve, and Gromov–Witten Invariants of Fano Manifolds

Published online by Cambridge University Press:  20 November 2018

Takeo Nishinou
Takeo Nishinou*
Affiliation:
Department of Mathematics, Tohoku University, Sendai, Miyagi, Japan. email: nishinou@math.tohoku.ac.jp
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Abstract

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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.

Keywords

14J45Fano varietiesGromov–Witten invariantstropical curves
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 67 , Issue 3 , 01 June 2015 , pp. 667 - 695
Copyright
Copyright © Canadian Mathematical Society 2015

References

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