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, MR 1969204, Zbl 1069.14019.

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]