Quiver moduli spaces of a given dimension
Representation Theory
2023-12-27 v3 Commutative Algebra
Algebraic Geometry
Abstract
It is shown that certain transformations on quiver-dimension vector pairs induce isomorphisms on the corresponding moduli spaces of quiver representations and map a stable dimension vector to a stable dimension vector. This result combined with a combinatorial analysis of dimension vectors in the fundamental set of a wild quiver is applied to prove that in each dimension there are only finitely many projective algebraic varieties occurring as a moduli space of representations of a quiver with a dimension vector that satisfies some simple constraints.
Cite
@article{arxiv.2303.08522,
title = {Quiver moduli spaces of a given dimension},
author = {M. Domokos},
journal= {arXiv preprint arXiv:2303.08522},
year = {2023}
}
Comments
v3: extensive revision