Summary: Problem Set 16
In an earlier problem set, it was shown that any three points in A2
can be
moved to any other set by an ane change of coordinates. The next problem is a
similar problem in Pn
. Let V Pn
be a set of points. V is said to be in linearly
general position if any subset of V of size n + 1 does not lie on a hyperplane
and if any subset of V of size k n does not lie on a k - 1-plane.
Problem 1. Prove that any 2 ordered sets of n + 2 points in linearly general
position in Pn
are projectively equivalent.
Problem 2. Can you nd a condition that allows you to determine when 4 points
in P1
are projectively equivalent? Hint: Let the two sets be {P1, P2, P3, P4} and
{Q1, Q2, Q3, Q4}. Move P1 to 1, move P2 to , and move P3 to 0. Where does
P4 get moved?
A modication of this procedure can be used to determine when n+3 ordered
points in Pn
are linearly equivalent (see pages 7,8,12 of Harris). An explicit answer

Source: Abo, Hirotachi - Department of Mathematics, University of Idaho

Collections: Mathematics