科研之友
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摘要
The Hitchin morphism is a map from the moduli space of Higgs bundles M-X to the Hitchin base B-X, where X is a smooth projective variety. When X has dimension at least two, this morphism is not surjective in general. Recently, Chen-Ngo introduced a closed subscheme A(X) of B-X, which is called the space of spectral data. They proved that the Hitchin morphism factors through A(X) and conjectured that A(X) is the image of the Hitchin morphism. We prove that when X is a smooth projective surface, this conjecture is true for vector bundles. Moreover, we show that A(X), for any dimension, is invariant under any proper birational morphism and apply the result to study A(X) for ruled surfaces.
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单位中山大学
