We explore the cohomological structure for the (possibly singular) moduli of SLn${\mathrm{SL}}_n$${\mathrm{SL}}_n$-Higgs bundles for arbitrary degree on a genus g$g$$g$ curve with respect to an effective divisor of degree >2g−2$>2g-2$$>2g-2$. We prove a support theorem for the SLn${\mathrm{SL}}_n$${\mathrm{SL}}_n$-Hitchin fibration extending de Cataldo's support theorem in the nonsingular case, and a version of the Hausel–Thaddeus topological mirror symmetry conjecture for intersection cohomology. This implies a generalization of the Harder–Narasimhan theorem concerning semistable vector bundles for any degree.

中文翻译：

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关于曲线上 SLn$\mathrm{SL}_n$-Higgs 丛模的交上同调

我们探索（可能是奇异的）模的上同调结构SLn${\mathrm{SL}}_n$${\mathrm{SL}}_n$- 一个属的任意程度的希格斯束G$G$$g$关于度数的有效除数的曲线> 2克− 2$>2G-2$$>2g-2$. 我们证明了一个支持定理SLn${\mathrm{SL}}_n$${\mathrm{SL}}_n$-Hitchin 纤维化在非奇异情况下扩展了 de Cataldo 的支持定理，以及交叉上同调的 Hausel-Thaddeus 拓扑镜像对称猜想的一个版本。这意味着 Harder-Narasimhan 定理关于任何程度的半稳定向量丛的推广。