Algebraic Geometry
Rings of invariants for representations of quivers
Comptes Rendus. Mathématique, Volume 340 (2005) no. 2, pp. 135-140.

In this Note we compute the generators of the ring of invariants for quiver factorization problems, generalizing results of Le Bruyn and Procesi. In particular, we find a necessary and sufficient combinatorial criterion for the projectivity of the associated invariant quotients. Further, we show that the non-projective quotients admit open immersions into projective varieties, which still arise from suitable quiver factorization problems.

Dans cette Note nous calculons les générateurs des anneaux d'invariants pour certains problèmes de factorisation associés aux représentations de carquois, généralisant un résultat démontré par Le Bruyn et Procesi. En particulier, nous déduisons un critère combinatoire nécéssaire et suffisant pour la projectivité du quotient. En plus, nous démontrons que les quotients non-projectifs peuvent être immergés de manière ouverte dans varietés projectives qui proviennent elles mêmes de problèmes de factorisation de carquois appropriés.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2004.12.012
Halic, Mihai 1; Stupariu, Mihai-Sorin 1

1 Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
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Halic, Mihai; Stupariu, Mihai-Sorin. Rings of invariants for representations of quivers. Comptes Rendus. Mathématique, Volume 340 (2005) no. 2, pp. 135-140. doi : 10.1016/j.crma.2004.12.012. http://www.numdam.org/articles/10.1016/j.crma.2004.12.012/

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