The connectedness of some varieties and the Deligne-Simpson problem
| dc.creator | Kostov, Vladimir Petrov | |
| dc.date | 2002-06-09 | |
| dc.date | 2003-06-03 | |
| dc.date.accessioned | 2026-07-07T04:49:00Z | |
| dc.date.available | 2026-07-07T04:49:00Z | |
| dc.description | The Deligne-Simpson problem (DSP) (resp. the weak DSP) is formulated like this: {\em give necessary and sufficient conditions for the choice of the conjugacy classes $C_j\subset GL(n,{\bf C})$ or $c_j\subset gl(n,{\bf C})$ so that there exist irreducible (resp. with trivial centralizer) $(p+1)$-tuples of matrices $M_j\in C_j$ or $A_j\in c_j$ satisfying the equality $M_1... M_{p+1}=I$ or $A_1+... +A_{p+1}=0$}. The matrices $M_j$ and $A_j$ are interpreted as monodromy operators of regular linear systems and as matrices-residua of Fuchsian ones on Riemann's sphere. For $(p+1)$-tuples of conjugacy classes one of which is with distinct eigenvalues 1) we prove that the variety $\{(M_1,..., M_{p+1})|M_j\in C_j,M_1... M_{p+1}=I\}$ or $\{(A_1,..., A_{p+1})|A_j\in c_j,A_1+... +A_{p+1}=0\}$ is connected if the DSP is positively solved for the given conjugacy classes and 2) we give necessary and sufficient conditions for the positive solvability of the weak DSP. | |
| dc.identifier | https://arxiv.org/abs/math/0206087 | |
| dc.identifier | http://arxiv.org/abs/math/0206087 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64263 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Rings and Algebras | |
| dc.subject | Representation Theory | |
| dc.title | The connectedness of some varieties and the Deligne-Simpson problem | |
| dc.type | text |