Some examples related to the Deligne-Simpson problem

2000/11/02 by Vladimir Petrov Kostov
Mathematics · #math.AG

paper · pdf

published as Proc2ndIntConfGeomIntQuant, Coral Press (2001) 208-227 · To appear in the proceedings of the Second International Confer ence on Geometry, Integrability and Quantization

arxiv created 2000/11/02 · arxiv updated 2009/11/30

Abstract

We consider the variety of (p+1)-tuples of matrices M_j from given conjugacy classes from GL(n,\bf C) such that M₁... 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.

Related

• Examples illustrating some aspects of the weak Deligne-Simpson pro blem
• The Deligne-Simpson problem -- a survey
• On the Deligne-Simpson problem
• On some aspects of the Deligne-Simpson problem
• Some examples of rigid representations