On the resultant of three ternary quadratic forms

by Markus Rost (Notes, November 2018, 12 pages)

The text contains a comparatively simple presentation of the resultant of three ternary quadratic forms.

[A presentation of the resultant of three ternary quadratic
forms]

In concrete terms the resultant is the Pfaffian of an alternating 8x8 matrix. Explicit computations identify that matrix with the one in

Eisenbud, Schreyer and Weyman; Resultants and Chow forms via exterior syzygies. J. Amer. Math. Soc. 16 (2003), no. 3, 537-579, MR1969204

Full text (version of Dec 4, 2018): [pdf]

On the discriminant of binary forms

by Markus Rost (Notes, September 2011/November 2018, 7 pages)

The discriminant of a binary form f of degree d is presented as the determinant of a (2d-2)x(2d-2)-matrix which is linear in the coefficients of f. There are no denominators and the method works over any ring in a coordinate free way. The construction has a natural explanation in terms of jet spaces.

[The discriminant of a binary form]

Explicitly, for a cubic binary form:

[A formula for the discriminant of a cubic binary form]

Full text (version of Dec 5, 2018): [pdf]