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 submersion on every stratum. Each stratum carries a canonical relative holomorphic symplectic form. These forms determine a vertical holomorphic Poisson bracket on the reduced structure sheaf, whose symplectic leaves are the connected orbit-type strata in the fibers. On each fiber, the Hitchin--Kobayashi correspondence is biholomorphic on every stratum and identifies its hyperk\"ahler structure. The harmonic representatives and vertical hyperk\"ahler tensors vary smoothly along the strata of the total space.
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...
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...
We prove that the tangent sheaf of $\SU_C(n,L)$ is slope stable for every smooth complex projective curve $C$ of genus $g\geq2$, every $n\geq2$, and every determinant $L$. For $g\geq3$, we prove a more general stability theorem on moduli spaces of principal bundles for connected reductive groups, using cohomology sheav...
Lagrangians of the moduli space of Higgs bundles are a fundamental piece of its study under the lens of mirror symmetry. We construct a new class of Lagrangians defined via a zero'velocity condition'imposed on the natural action of the non-zero complex numbers on the moduli space, motivated by a certain'infinitesimal c...
P. Gothen, André G. Oliveira, R. Pereira· 0 citations
We study Fourier-Mukai duality for a class of compactified Prym fibrations including moduli spaces of $\mathrm{SL}$ Higgs bundles over the elliptic locus. This leads to a shadow of the Hausel-Thaddeus conjecture, proof of the Corti-Hanamura motivic decomposition conjecture for these fibrations, and multiplicativity of...
We prove that the rational Chow ring of every connected component of the multi-scale compactifications of the genus three strata $\mathcal{H}(4), \mathcal{H}(2,2)$ and $\mathcal{H}(3,1)$ is generated by boundary-stratum classes. Our proof shows Chow-K\"unneth generation property of boundary strata of the multi-scale co...
P. Devkota, Myeongjae Lee· 1 citation
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