2014/02/20 by M. Domokos, Domokos, M., Dániel Joó +1
Mathematics · #14M25 14L24 16G20 52B20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT) #math.AC #math.AG #math.RT #msc:14L24 #msc:14M25 #msc:16G20 #msc:52B20
paper · pdf · doi:10.48550/arxiv.1402.5096
arxiv created 2014/02/20 · openalex publication_date 2014/02/20 · arxiv updated 2014/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Toric quiver varieties (moduli spaces of quiver representations) are studied. Given a quiver and a weight there is an associated quasiprojective toric variety together with a canonical embedding into projective space. It is shown that for a quiver with no oriented cycles the homogeneous ideal of this embedded projective variety is generated by elements of degree at most 3. In each fixed dimension d up to isomorphism there are only finitely many d-dimensional toric quiver varieties. A procedure for their classification is outlined.