Some examples related to the Deligne-Simpson problem
Abstract
We consider the variety of (p+1)-tuples of matrices Mj from given conjugacy classes from GL(n, C) such that M1... Mp+1=I. This variety is connected with the Deligne-Simpson problem and the matrices Mj are interpreted as monodromy operators of regular systems on Riemann's sphere. We consider among others cases when the dimension of the variety is higher than the expected one due to the presence of (p+1)-tuples with non-trivial centralizers.
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