论文标题
与成对矩阵相关的未成年人理想的最小免费分辨率
Minimal free resolutions of ideals of minors associated to pairs of matrices
论文作者
论文摘要
考虑由固定尺寸的矩阵$（a，b）组成的仿射空间，以及其按等级条件$ \ perperatorName {rank} a \ leq a $，$ \ operatorName {rank rank} b \ leq leq b $ and $ leq b $ and $ \ leq b $ and $ \ perperatornAme {rankorname {等级{ $ a，b，c $。这些品种恰恰是$ a_3 $颤动的表示轨道的轨道封闭。在本文中，我们构建了此类品种定义理想的（模棱两可的）最小的自由分辨率。我们展示了这个问题是如何等同于确定两步标志品种上重言式捆绑包的两个Schur函子的张量产物的共同体学组。我们为确定这些群体的确定提供了几种技术，这些技术具有独立的兴趣。
Consider the affine space consisting of pairs of matrices $(A,B)$ of fixed size, and its closed subvariety given by the rank conditions $\operatorname{rank} A \leq a$, $\operatorname{rank} B \leq b$ and $\operatorname{rank} (A\cdot B) \leq c$, for three non-negative integers $a,b,c$. These varieties are precisely the orbit closures of representations for the equioriented $A_3$ quiver. In this paper we construct the (equivariant) minimal free resolutions of the defining ideals of such varieties. We show how this problem is equivalent to determining the cohomology groups of the tensor product of two Schur functors of tautological bundles on a 2-step flag variety. We provide several techniques for the determination of these groups, which is of independent interest.
