Math 8205
Spring 1998

Hint for Part b. of Exercise 6

There are two cases to consider: In the first case, it would be nice to  show that we can choose  L  so that each point of  L  lies on at most finitely many secant lines of  X.  One way to accomplish this is to consider the closed subset  Z \subset Sec X,  defined to be the closure of the following subset:


Z0 = {z : z \in Sec X  and  z  lies on infinitely secant lines  <p,q>,  p \in X  and  q \in X}.
Specifically, one can estimate the dimension of  Z, showing that  dim Z \leq 2r - 1.

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