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The spectral base of Hitchin maps

组织者

黄鹏飞 , 苏桃 , 孙浩

演讲者

Jie Liu

时间

2024年03月20日 10:00 至 11:00

地点

A3-2-303

线上

Zoom 518 868 7656 (BIMSA)

摘要

Let $X$ be a projective manifold. The Hitchin morphism is a map from the moduli stack of Higgs bundles over $X$ to the Hitchin base, which sends a Higgs bundle to its characteristic polynomial. If $X$ is a curve, it is well-known that the Hitchin morphism is surjective and it plays an important role in the study of the moduli space of Higgs bundles. However, if $X$ has dimension at least two, the Hitchin morphism in general is not surjective. Thus a closed subset of the Hitchin base, called the spectral base, is introduced by Tsao-Hsien Chen and Bao Chau Ngo and it is conjectured that the Hitchin morphism is onto the spectral base. This conjecture is confirmed when $X$ is a surface by the works of Tsao-Hsien Chen and Bao Chau Ngo and Lei Song and Hao Sun. In this talk, I will present our solution to this conjecture for rank two Higgs bundles and also show the vanishing of the spectral base for Hermitian locally symmetric spaces with higher rank. This is joint work with Siqi He and Ngaiming Mok.