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Enumerate tropical algebraic curves

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  • 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.)
  • Received : 2017.01.07
  • Accepted : 2017.06.20
  • Published : 2017.06.30

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

Acknowledgement

Supported by : Sungshin Women’s University

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