 
Summary: Chow forms
Chris Peterson and Hirotachi Abo
Note. This script is also available at:
http://www.math.colostate.edu/~abo/Research/smi/smialgebraicgeometry.html
1. Chow form of a line in P3
Let k be an algebraically closed field, let P3
be the threedimensional pro
jective space over k. We denote by S the homogeneous coordinate ring
k[x0, x1, x2, x3] of P3
. Fix a line L in P3
. The general line in P3
does not
intersect L. So the lines in P3
hitting L form a proper subset C(L) (actually
a subvariety) of the grassmaniann of lines in P3
. A question is: "How can we
describe this subset?" Assume that the ideal I(L) of L is generated by the
following two linear forms: 3
i=0 a0ixi and 3
i=0 a1ixi. Let L be a line in P3
