论文标题
向量束和图电位的模量空间的分解
Decompositions of moduli spaces of vector bundles and graph potentials
论文作者
论文摘要
我们提出了一个猜想的半三相分解，该分解是稳定秩2束的模量空间的衍生类别，具有固定的奇数决定因素，由narasimhan独立表达。我们讨论了一些证据，还提出了具有其他结构的半三相分解。 我们还讨论了另外两个分解。一个是在粒度圆形的圆环中的这个模量空间的分解，它与各种已知的动机分解有关。另一个是图电位给出的候选镜像Landau-Ginzburg模型的临界价值分解，这反过来又与Munoz的量子同胞分解有关。这对应于福卡亚类别的正交分解。我们将解释如何将这些分解作为猜想的半双胞异式分解的证据。
We propose a conjectural semiorthogonal decomposition for the derived category of the moduli space of stable rank 2 bundles with fixed determinant of odd degree, independently formulated by Narasimhan. We discuss some evidence for, and furthermore propose semiorthogonal decompositions with additional structure. We also discuss two other decompositions. One is a decomposition of this moduli space in the Grothendieck ring of varieties, which relates to various known motivic decompositions. The other is the critical value decomposition of a candidate mirror Landau-Ginzburg model given by graph potentials, which in turn is related under mirror symmetry to Munoz's decomposition of quantum cohomology. This corresponds to an orthogonal decomposition of the Fukaya category. We will explain how these decompositions can be seen as evidence for the conjectural semiorthogonal decomposition.
