论文标题
Higgs捆绑包的模量和模量的同时$χ$独立于模量
Cohomological $χ$-independence for moduli of one-dimensional sheaves and moduli of Higgs bundles
论文作者
论文摘要
我们证明，与在摩尔板表面上足够的曲线类别中支撑的一维半相关的滑轮的模量空间的交点共同体（以及偏见和霍奇过滤）独立于支撑膜的欧拉特征。对于有效的除数$ d $ a $ \ mathrm {deg}（d）> 2G-2 $，我们还证明了可半固定捆绑的模量捆绑的模量空间的类似结果。我们的结果证实了Bousseau的共同学$χ$独立的猜想，以$ \ MATHBB {P}^2 $，并验证Toda对Gopakumar-Vafa不变性的猜想对于某些局部曲线和本地表面。 为了证明证明，我们将NGô的支持定理的广义版，对堆积的Hilbert-Chow Morphism的维度估算，以及从Moduli堆栈的形态分裂的定理与良好的Git商。
We prove that the intersection cohomology (together with the perverse and the Hodge filtrations) for the moduli space of one-dimensional semistable sheaves supported in an ample curve class on a toric del Pezzo surface is independent of the Euler characteristic of the sheaves. We also prove an analogous result for the moduli space of semistable Higgs bundles with respect to an effective divisor $D$ of degree $\mathrm{deg}(D)>2g-2$. Our results confirm the cohomological $χ$-independence conjecture by Bousseau for $\mathbb{P}^2$, and verify Toda's conjecture for Gopakumar-Vafa invariants for certain local curves and local surfaces. For the proof, we combine a generalized version of Ngô's support theorem, a dimension estimate for the stacky Hilbert-Chow morphism, and a splitting theorem for the morphism from the moduli stack to the good GIT quotient.
