论文标题
通过稳定性和翻转的变化，曲线上束的模量空间的动机
Motives of moduli spaces of bundles on curves via variation of stability and flips
论文作者
论文摘要
我们研究了具有额外结构（例如抛物线结构或希格斯场）的平滑投影曲线上某些模量载体束的合理杂志动机。在抛物线情况下，这些模量空间取决于重量给出的稳定性条件的选择。我们的方法是使用简单的birational变换（标准触发器/拖鞋和Mukai拖鞋）来使用这种稳定条件变化的明确描述，我们了解了Chow动机的变化。对于抛物线矢量束的模量空间，我们描述了墙壁交叉下动机的变化，对于抛物线式希格斯捆绑包的模量空间，我们表明动机在壁交叉下没有变化。此外，我们证明了一个较硬和纳拉西姆汉的经典定理的动机类似物，该定理与具有和没有固定决定性的矢量捆绑包的模量空间的理性共同体相关。对于等级2的奇数矢量束，我们获得了可半轴向载体束的模量空间的合理食物动机，Higgs捆绑包的模量空间和抛物线（Higgs）捆绑包的模量空间，这些空间（Higgs）捆绑涉及对一般权重（与固定确定性的无关）。
We study the rational Chow motives of certain moduli spaces of vector bundles on a smooth projective curve with additional structure (such as a parabolic structure or Higgs field). In the parabolic case, these moduli spaces depend on a choice of stability condition given by weights; our approach is to use explicit descriptions of variation of this stability condition in terms of simple birational transformations (standard flips/flops and Mukai flops) for which we understand the variation of the Chow motives. For moduli spaces of parabolic vector bundles, we describe the change in motive under wall-crossings, and for moduli spaces of parabolic Higgs bundles, we show the motive does not change under wall-crossings. Furthermore, we prove a motivic analogue of a classical theorem of Harder and Narasimhan relating the rational cohomology of moduli spaces of vector bundles with and without fixed determinant. For rank 2 vector bundles of odd degree, we obtain formulas for the rational Chow motives of moduli spaces of semistable vector bundles, moduli spaces of Higgs bundles and moduli spaces of parabolic (Higgs) bundles that are semistable with respect to a generic weight (all with and without fixed determinant).
