Complete intersection quiver settings with one dimensional vertices
Representation Theory
2015-03-19 v2 Algebraic Geometry
Abstract
We describe the class of quiver settings with one dimensional vertices whose semi-simple representations are parametrized by a complete intersection variety. We show that these quivers can be reduced to a one vertex quiver with some combinatorial reduction steps. We also show that this class consists of the quivers from which we can not obtain two specific non complete intersection quivers via contracting strongly connected components and deleting subquivers. The class of coregular quiver settings with arbitrary dimension vector, that has been described by an earlier result via reduction steps, can also be characterized by not containing a specific subquiver in the above sense.
Cite
@article{arxiv.1105.3067,
title = {Complete intersection quiver settings with one dimensional vertices},
author = {Dániel Joó},
journal= {arXiv preprint arXiv:1105.3067},
year = {2015}
}