Constructs a flat degeneration of the Higgs bundle moduli stack on curves with intrinsic log-symplectic form, flat Hitchin map with complete fibers, and Lagrangian nilpotent cone locus, extended over stable curves.
Derived log stacks after Olsson
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abstract
In this note, we give a formulation of log structures for derived stacks using Olsson's log stack. The derived cotangent complex is then Olsson's logarithmic cotangent complex, which (unlike Gabber's) is just given by log differential forms in the log smooth case. The derived moduli stack of log stable maps then produces the desired virtual tangent space and obstruction theory on the underlying underived stack.
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math.AG 1years
2023 1verdicts
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Moduli stacks of Higgs bundles on stable curves
Constructs a flat degeneration of the Higgs bundle moduli stack on curves with intrinsic log-symplectic form, flat Hitchin map with complete fibers, and Lagrangian nilpotent cone locus, extended over stable curves.