For the standard representation of Sp_{2n}(C), the Gaiotto locus is the Bialynicki-Birula closure associated to U(Sp_{2n-2}(C)) inside the nilpotent cone, and its intersection with the stable cotangent chart is the closure of the conormal bundle to the one-spinor stratum of the generalized theta-div
Duke Math
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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.
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Gaiotto Loci and the Nilpotent Cone for $\mathrm{Sp}_{2n}(\mathbb C)$
For the standard representation of Sp_{2n}(C), the Gaiotto locus is the Bialynicki-Birula closure associated to U(Sp_{2n-2}(C)) inside the nilpotent cone, and its intersection with the stable cotangent chart is the closure of the conormal bundle to the one-spinor stratum of the generalized theta-div
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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.