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
Geometry of the moduli space of
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A surjective commutative forgetful diagram exists from the C*-flip chain of moduli spaces of O_X-twisted rank 2 constrained framed Hitchin pairs to the C*-flip chain of moduli spaces of rank 2 framed modules on a smooth complex projective curve.
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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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A chain of $\mathbb{C}^{*}$-flips of the moduli spaces of $\mathcal{O}$-twisted rank 2 constrained framed Hitchin pairs on a smooth curve
A surjective commutative forgetful diagram exists from the C*-flip chain of moduli spaces of O_X-twisted rank 2 constrained framed Hitchin pairs to the C*-flip chain of moduli spaces of rank 2 framed modules on a smooth complex projective curve.