Some examples related to the Deligne-Simpson problem

Details Some examples related to the Deligne-Simpson problem Some examples related to the Deligne-Simpson problem

2000-11-02

arxiv.org/abs/math/0011015v1

Proc2ndIntConfGeomIntQuant, Coral Press (2001) 208-227

Mathematics

Algebraic Geometry

To appear in the proceedings of the Second International Confer ence on Geometry, Integrability and Quantization

Scientific paper

We consider the variety of $(p+1)$-tuples of matrices $M_j$ from given conjugacy classes from $GL(n,{\bf C})$ such that $M_1... M_{p+1}=I$. This variety is connected with the Deligne-Simpson problem and the matrices $M_j$ 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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