基于相交理论的非Schurian不可分解性
Non-Schurian indecomposables via intersection theory
摘要：
对于一个非循环的三个顶点，我们考虑了一个非Schurian根的典型分解和相关的某些表示的广义Kronecker图。这些表示对应于包含在交叉点的两个子品种的格拉斯曼和产生的表示原始的birds，保持不可分解性。我们表明，这些子簇相交使用舒伯特演算。假设交集包含一个Schurian表示，它已经包含了一个Schurian表示的开子集，其维数是我们通过Kac定理所期望的。
英文摘要：
For an acyclic quiver with three vertices, we consider the canonical decomposition of a non-Schurian root and associate certain representations of a generalized Kronecker quiver. These representations correspond to points contained in the intersection of two subvarieties of a Grassmannian and give rise to representations of the original quiver, preserving indecomposability. We show that these subvarieties intersect using Schubert calculus. Provided that the intersection contains a Schurian representation, it already contains an open subset of Schurian representations whose dimension is what we expect by Kac's Theorem.
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