Mixed discriminants

• The mixed discriminant of Laurent polynomials in 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 -discriminant. We show that the degree of the mixed discriminant is a piecewise linear function in the Plucker coordinates of a mixed Grassmannian. An explicit degree formula is given for the case of plane curves.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

A-discriminant

Degree

Multiple root

Cayley polytope

Tropical discriminant

Matroid strata

Mixed Grassmannian

Publication and Content Type

ref (subject category)

art (subject category)