Revista Matemática Iberoamericana

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Volume 24, Issue 3, 2008, pp. 941–961
DOI: 10.4171/RMI/561

Published online: 2008-12-31

Tropical resultants for curves and stable intersection

Luis Felipe Tabera Alonso[1]

(1) 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.

Keywords: Tropical geometry, resultants, plane curves

Tabera Alonso Luis Felipe: Tropical resultants for curves and stable intersection. Rev. Mat. Iberoam. 24 (2008), 941-961. doi: 10.4171/RMI/561