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http://dx.doi.org/10.14477/jhm.2017.30.3.185
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Enumerate tropical algebraic curves |

Kim, Young Rock
(Major in Mathematics Education, Graduate School of Education, Hankuk University of Foreign Studies)
Shin, Yong-Su (Dept. of Math., Sungshin Women's Univ.) |

Publication Information

Abstract

In tropical geometry, the sum of two numbers is defined as the minimum, and the multiplication as the sum. As a way to build tropical plane curves, we could use Newton polygons or amoebas. We study one method to convert the representation of an algebraic variety from an image of a rational map to the zero set of some multivariate polynomials. Mikhalkin proved that complex curves can be replaced by tropical curves, and induced a combination formula which counts the number of tropical curves in complex projective plane. In this paper, we present close examinations of this particular combination formula.

Keywords

tropical geometry; Newton polygon; amoeba; The number of tropical curves; Gromov-Witten invariants;

Citations & Related Records

Times Cited By KSCI :
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