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Mixed discriminants |
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| Authors: | Eduardo Cattani María Angélica Cueto Alicia Dickenstein Sandra Di Rocco Bernd Sturmfels |
| Institution: | 1. Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, 01003, USA 2. FB12 Institut für Mathematik, Goethe-Universit?t Frankfurt, Robert-Mayer-Str. 6-8, 60325, Frankfurt am Main, Germany 3. Departamento de Matemática, FCEN, Universidad de Buenos Aires and IMAS, CONICET, Ciudad Universitaria, Pab, I - C1428EGA, Buenos Aires, Argentina 4. KTH, Mathematics, S-10044, Stockholm, Sweden 5. Department of Mathematics, University of California, Berkeley, CA, 94720, USA |
| Abstract: | The mixed discriminant of $n$ Laurent polynomials in $n$ variables is the irreducible polynomial in the coefficients which vanishes whenever two of the roots coincide. The Cayley trick expresses the mixed discriminant as an $A$ -discriminant. We show that the degree of the mixed discriminant is a piecewise linear function in the Plücker coordinates of a mixed Grassmannian. An explicit degree formula is given for the case of plane curves. |
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