| 概要 | It is a simple but interesting problem to determine a minimal number of
chambers of real line arrangements belonging to some family. For example, a
family of arrangements the Ziegler restriction of which are the same, or
the numbers of lines and directions of which are fixed. The lower bound of
the former one can be obtained by Yoshinaga's criterion, and the minimal
chamber arrangement in this family is equivalent to the free arrangement.
In this talk we give that of the latter one and an easy sufficient
condition for the freeness in terms of minimal chamber arrangements in that
family. Also, the relation to the splitting type problem of rank two vector
bundles on the projective plane will be mentioned. |