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- W3100548889 abstract "We compute the monodromy of the Hitchin fibration for the moduli space of $L$-twisted $SL(n,mathbb{C})$ and $GL(n,mathbb{C})$-Higgs bundles for any $n$, on a compact Riemann surface of genus $g>1$. We require the line bundle $L$ to either be the canonical bundle or satisfy $deg(L) > 2g-2$. The monodromy group is generated by Picard-Lefschetz transformations associated to vanishing cycles of singular spectral curves. We construct such vanishing cycles explicitly and use this to show that the $SL(n,mathbb{C})$ monodromy group is a {em skew-symmetric vanishing lattice} in the sense of Janssen. Using the classification of vanishing lattices over $mathbb{Z}$, we completely determine the structure of the monodromy groups of the $SL(n,mathbb{C})$ and $GL(n,mathbb{C})$ Hitchin fibrations. As an application we determine the image of the restriction map from the cohomology of the moduli space of Higgs bundles to the cohomology of a non-singular fibre of the Hitchin fibration." @default.
- W3100548889 created "2020-11-23" @default.
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- W3100548889 date "2017-10-31" @default.
- W3100548889 modified "2023-10-15" @default.
- W3100548889 title "Monodromy of the SL(n) and GL(n) Hitchin fibrations" @default.
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- W3100548889 doi "https://doi.org/10.1007/s00208-017-1611-6" @default.
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