LAUSR

Abstract We consider the space of binary cubic forms, equipped with the natural action of the group GL2 of invertible linear transformations of We describe explicitly the category of GL2-equivariant coherent -modules as the category of representations of a quiver with relations. We show moreover that this quiver is of tame representation type and we classify its indecomposable representations. We also give a construction of the simple equivariant -modules (of which there are 14), and give formulas for the characters of their underlying GL2-representations. We conclude the article with an explicit calculation of (iterated) local cohomology groups with supports given by orbit closures.