论文标题
（co） - 非kähler椭圆形表面上的希格斯捆绑包
(Co)-Higgs bundles on Non-Kähler Elliptic Surfaces
论文作者
论文摘要
在本文中，我们在非kähler椭圆形表面上研究了希格斯和共同的捆绑包。我们特别表明，仅当椭圆纤维的基部至少具有两个属并使用这种存在的结果来提供明确的拓扑条件，从而确保了稳定级别2杆的平滑度，仅当椭圆纤维的底部至少具有两个属的属时，才表明，非平凡的稳定希格束存在。我们还表明，仅当椭圆纤维的底部具有0属0时，非平凡的稳定共同束束存在，在这种情况下，非Kähler椭圆表面是HOPF表面。然后，我们对等级2案件中的非平凡共同捆绑包进行了完整的描述；这些非平凡的Rank-2 Co-Higgs捆绑包是$ \ Mathbb {p}^1 $ - 捆绑在Hopf表面上的非平凡全态Poisson结构的示例。
In this paper, we study Higgs and co-Higgs bundles on non-Kähler elliptic surfaces. We show, in particular, that non-trivial stable Higgs bundles only exist when the base of the elliptic fibration has genus at least two and use this existence result to give explicit topological conditions ensuring the smoothness of moduli spaces of stable rank-2 sheaves on such surfaces. We also show that non-trivial stable co-Higgs bundles only exist when the base of the elliptic fibration has genus 0, in which case the non-Kähler elliptic surface is a Hopf surface. We then given a complete description of non-trivial co-Higgs bundles in the rank 2 case; these non-trivial rank-2 co-Higgs bundles are examples of non-trivial holomorphic Poisson structures on $\mathbb{P}^1$-bundles over Hopf surfaces.
