论文标题
Chen-Ruan的共同体和抛物线束模量空间的Orbifold Euler特征
Chen--Ruan cohomology and orbifold Euler characteristic of moduli spaces of parabolic bundles
论文作者
论文摘要
我们考虑稳定的抛物线式希格斯捆绑的模量空间和固定的决定因素，并在平滑的复杂的射击曲线$ x $ g $的$ g $的$ g \，$ g \，\ geqq \ geq \，2 $ 2 $上具有完整的标志准抛物线结构。 $ r $ $ $ $ $γ$ $ r $ torsion点的$ x $的$ r $ torsion积分在此模子空间上。我们描述了该模量各个固定点基因座的连接组件在$γ$的非平凡元素下。当希格斯字段为零，换句话说，当我们将自己限制在稳定的抛物线束的模量上时，我们还计算了相应的全局eRbifold的Orbifold Euler特征。我们还描述了在某些条件下在等级和程度的某些条件下的该Orbifold的Chen-Ruan共同体学，并在特殊情况下描述了Chen-Ruan产品结构。
We consider the moduli space of stable parabolic Higgs bundles of rank $r$ and fixed determinant, and having full flag quasi-parabolic structures over an arbitrary parabolic divisor on a smooth complex projective curve $X$ of genus $g$, with $g\,\geq\, 2$. The group $Γ$ of $r$-torsion points of the Jacobian of $X$ acts on this moduli space. We describe the connected components of the various fixed point loci of this moduli under non-trivial elements from $Γ$. When the Higgs field is zero, or in other words when we restrict ourselves to the moduli of stable parabolic bundles, we also compute the orbifold Euler characteristic of the corresponding global quotient orbifold. We also describe the Chen--Ruan cohomology groups of this orbifold under certain conditions on the rank and degree, and describe the Chen--Ruan product structure in special cases.
