Geodesic
Tropical discriminants
Dickenstein, Alicia1 ; Feichtner, Eva2, 3 ; Sturmfels, Bernd4
1 Departamento de Matemática, FCEN, Universidad de Buenos Aires, (1428) B. Aires, Argentina
2 Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland
3 Department of Mathematics, University of Stuttgart, 70569 Stuttgart, Germany
4 Department of Mathematics, University of California, Berkeley, California 94720
Journal of the American Mathematical Society, Tome 20 (2007) no. 4, pp. 1111-1133

Voir la notice de l'article provenant de la source American Mathematical Society

Tropical geometry is used to develop a new approach to the theory of discriminants and resultants in the sense of Gel$’$fand, Kapranov and Zelevinsky. The tropical $A$-discriminant is the tropicalization of the dual variety of the projective toric variety given by an integer matrix $A$. This tropical algebraic variety is shown to coincide with the Minkowski sum of the row space of $A$ and the tropicalization of the kernel of $A$. This leads to an explicit positive formula for all the extreme monomials of any $A$-discriminant.
DOI : 10.1090/S0894-0347-07-00562-0

Dickenstein, Alicia 1 ; Feichtner, Eva 2, 3 ; Sturmfels, Bernd 4

1 Departamento de Matemática, FCEN, Universidad de Buenos Aires, (1428) B. Aires, Argentina
2 Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland
3 Department of Mathematics, University of Stuttgart, 70569 Stuttgart, Germany
4 Department of Mathematics, University of California, Berkeley, California 94720 
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Dickenstein, Alicia; Feichtner, Eva; Sturmfels, Bernd. Tropical discriminants. Journal of the American Mathematical Society, Tome 20 (2007) no. 4, pp. 1111-1133. doi: 10.1090/S0894-0347-07-00562-0

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