Author

Shi-Yu Cao

3 papers indexed here

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Preprint Oct 2026

Asymptotics of the Moduli Spaces of Parabolic $\mathrm{SL}(3,\mathbb C)$-Higgs Bundles

We study the large-scale geometry of the moduli spaces of stable strongly parabolic $\mathrm{SL}(3,\C)$-Higgs bundles on the three-punctured sphere for a family of parabolic weights. We glue the local Toda model metric to a decoupled metric obtained from the spectral line bundle, and perturb the resulting approximate m...

Shi-Yu Cao · 0 citations

Preprint Sep 2026

An analytic construction of the universal moduli space of $\mathrm{SL}_r(\mathbb C)$-Higgs bundles

We construct the moduli space of marked polystable $\mathrm{SL}_r(\mathbb C)$-Higgs bundles via analytic methods. The resulting space is normal and Hausdorff, and its local models are products of a Teichm\"uller neighbourhood with a quotient of a quadratic cone. These models preserve the curve parameter and identify th...

Shi-Yu Cao · 0 citations

Preprint Sep 2026

Stratification of Joint Moduli Spaces of Higgs Bundles

We study the marked analytic moduli space of polystable degree-zero $\mathrm{SL}_r(\C)$-Higgs bundles over Teichm\"uller space. The connected components of the orbit-type loci defined by the full determinant-one stabilizers form a complex Whitney stratification. The projection to Teichm\"uller space is a holomorphic su...

Shi-Yu Cao · 0 citations