The Hitchin morphism for certain surfaces fibered over a curve
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909831217020928 |
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| author | Huynh, Matthew |
| author_facet | Huynh, Matthew |
| contents | The Chen-Ngô Conjecture predicts that the Hitchin morphism from the moduli stack of $G$-Higgs bundles on a smooth projective variety surjects onto the space of spectral data. The conjecture is known to hold for the group $GL_n$ and any surface, and for the group $GL_2$ and any smooth projective variety. We prove the Chen-Ngô Conjecture for any reductive group when the variety is a ruled surface or (a blowup of) a nonisotrivial elliptic fibration with reduced fibers. Furthermore, if the group is a classical group, i.e. $G \in \{SL_n,SO_n,Sp_{2n}\}$, then we prove the Hitchin morphism restricted to the Dolbeault moduli space of semiharmonic $G$-Higgs bundles surjects onto the space of spectral data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01874 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Hitchin morphism for certain surfaces fibered over a curve Huynh, Matthew Algebraic Geometry 14D20, 14J60 The Chen-Ngô Conjecture predicts that the Hitchin morphism from the moduli stack of $G$-Higgs bundles on a smooth projective variety surjects onto the space of spectral data. The conjecture is known to hold for the group $GL_n$ and any surface, and for the group $GL_2$ and any smooth projective variety. We prove the Chen-Ngô Conjecture for any reductive group when the variety is a ruled surface or (a blowup of) a nonisotrivial elliptic fibration with reduced fibers. Furthermore, if the group is a classical group, i.e. $G \in \{SL_n,SO_n,Sp_{2n}\}$, then we prove the Hitchin morphism restricted to the Dolbeault moduli space of semiharmonic $G$-Higgs bundles surjects onto the space of spectral data. |
| title | The Hitchin morphism for certain surfaces fibered over a curve |
| topic | Algebraic Geometry 14D20, 14J60 |
| url | https://arxiv.org/abs/2504.01874 |