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- Title
On the Image of Hitchin Morphism for Algebraic Surfaces: The Case GL<sub>n</sub>.
- Authors
Song, Lei; Sun, Hao
- Abstract
The Hitchin morphism is a map from the moduli space of Higgs bundles |$\mathscr {M}_{X}$| to the Hitchin base |$\mathscr {B}_{X}$| , where |$X$| is a smooth projective variety. When |$X$| has dimension at least two, this morphism is not surjective in general. Recently, Chen-Ngô introduced a closed subscheme |$\mathscr {A}_{X}$| of |$\mathscr {B}_{X}$| , which is called the space of spectral data. They proved that the Hitchin morphism factors through |$\mathscr {A}_{X}$| and conjectured that |$\mathscr {A}_{X}$| 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 |$\mathscr {A}_{X}$| , for any dimension, is invariant under any proper birational morphism and apply the result to study |$\mathscr {A}_{X}$| for ruled surfaces.
- Subjects
VECTOR bundles; ALGEBRAIC surfaces; MORPHISMS (Mathematics); LOGICAL prediction
- Publication
IMRN: International Mathematics Research Notices, 2024, Vol 2024, Issue 1, p492
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnad043