Let be a finitely generated associative algebra over an algebraically closed field , and consider the variety of -module structures on . In case is of finite representation type, equations defining the closure are known for ; they are given by rank conditions on suitable matrices associated with . We study the schemes defined by such rank conditions for modules over arbitrary , comparing them with similar schemes defined for representations of quivers and obtaining results on singularities. One of our main theorems is a description of the ideal of for a representation of a quiver of type , a result Lakshmibai and Magyar established for the equioriented quiver of type in .
Cite this article
Christine Riedtmann, Grzegorz Zwara, Orbit closures and rank schemes. Comment. Math. Helv. 88 (2013), no. 1, pp. 55–84DOI 10.4171/CMH/278