Quiver moduli spaces of a given dimension

2023/03/15 by M. Domokos, Domokos, M.
Mathematics · #16G20 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 14L24 #Representation Theory (math.RT) #Secondary 13A50

paper · pdf · doi:10.48550/arxiv.2303.08522

openalex publication_date 2023/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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