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.
@article{1228834299,
author = {Tabera
,
Luis Felipe},
title = {Tropical resultants for curves and stable intersection},
journal = {Rev. Mat. Iberoamericana},
volume = {24},
number = {2},
year = {2008},
pages = { 941-961},
language = {en},
url = {http://dml.mathdoc.fr/item/1228834299}
}
Tabera
,
Luis Felipe. Tropical resultants for curves and stable intersection. Rev. Mat. Iberoamericana, Tome 24 (2008) no. 2, pp. 941-961. http://gdmltest.u-ga.fr/item/1228834299/