Tropical discriminants

• Autores: Alicia Dickenstein, Eva María Feichtner, Bernd Sturmfels
• Localización: Journal of the American Mathematical Society, ISSN 0894-0347, Vol. 20, Nº 4, 2007, págs. 1111-1133
• Idioma: inglés
• DOI: 10.1090/s0894-0347-07-00562-0
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• Resumen

  • 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.