Revista Matemática Iberoamericana

Tropical resultants for curves and stable intersection

Luis Felipe Tabera

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Abstract

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 information

Source
Rev. Mat. Iberoamericana Volume 24, Number 3 (2008), 941-961.

Dates
First available in Project Euclid: 9 December 2008

Permanent link to this document
http://projecteuclid.org/euclid.rmi/1228834299

Mathematical Reviews number (MathSciNet)
MR2490204

Zentralblatt MATH identifier
05509268

Subjects
Primary: 14M25: Toric varieties, Newton polyhedra [See also 52B20] 14H50: Plane and space curves 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]

Keywords
tropical geometry resultants plane curves

Citation

Tabera , Luis Felipe. Tropical resultants for curves and stable intersection. Rev. Mat. Iberoamericana 24 (2008), no. 3, 941--961. http://projecteuclid.org/euclid.rmi/1228834299.


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