Equivariant -modules on binary cubic forms
Equivariant -modules on binary cubic forms
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二元三次形式上的等变模
作者：
A. Lorincz;Claudiu Raicu;J. Weyman
本文考虑二元三次型空间，其可逆线性变换群GL 2的自然作用是：.我们明确地把GL 2-等变相干模范畴描述为具有关系的模的表示范畴。此外，我们表明，这是驯服的表示型，我们分类其不可分解的表示。给出了单等变-模（共14个）的构造，并给出了它们的GL ~ 2-表示的特征标的公式。最后，我们明确计算（迭代）局部上同调群与轨道闭包的支持。
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.