On the intersection cohomology of the moduli of SLn$\mathrm{SL}_n$‐Higgs bundles on a curve
On the intersection cohomology of the moduli of SLn$\mathrm{SL}_n$‐Higgs bundles on a curve
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曲线上 SLn$mathrm{SL}_n$−希格斯丛模的交交上同调
DOI：
10.1112/topo.12250
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发表时间：
2022
影响因子：
1.1
通讯作者：
Shen, Junliang
中科院分区：
文献类型：
--
作者：
Maulik, Davesh;Shen, Junliang
我们研究了亏格g$g$曲线上任意次的SLn$\mathm{SL}_n$-Higgs丛关于>；2g−2$>；2g-2$的有效因子的(可能奇异的)模的上同调结构。证明了SLn$\mathm{SL}_n$-Hitchin纤维在非奇异情形下推广了de Cataldo的支撑定理，并证明了Hausel-Thaddeus上同调拓扑镜对称猜想的一个形式.这意味着Harder-Narasimhan关于任意阶半稳定向量丛的定理的推广。我们的主要工具是最近建立的Ngô型支撑不等式，它适用于可能奇异的环境空间和交上同调复形。
We explore the cohomological structure for the (possibly singular) moduli of SLn$\mathrm{SL}_n$‐Higgs bundles for arbitrary degree on a genus g$g$ curve with respect to an effective divisor of degree >2g−2$>2g-2$. We prove a support theorem for the SLn$\mathrm{SL}_n$‐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.Our main tool is an Ngô–type support inequality established recently which works for possibly singular ambient spaces and intersection cohomology complexes.