Tropical resultants for curves and stable intersection

  • Luis Felipe Tabera Alonso

    Universidad de Cantabria, Santander, Spain


We introduce the notion of resultant of two planar curves in the tropical geometry framework. We prove that the tropicalization of the algebraic resultant can be used to compute the stable intersection of two tropical plane curves. It is shown that, for two generic preimages of the curves to an algebraic framework, their intersection projects exactly onto the stable intersection of the curves. It is also given sufficient conditions for such a generality in terms of the residual coefficients of the algebraic coefficients of defining equations of the curves.

Cite this article

Luis Felipe Tabera Alonso, Tropical resultants for curves and stable intersection. Rev. Mat. Iberoam. 24 (2008), no. 3, pp. 941–961

DOI 10.4171/RMI/561