The GIT boundary of quintic threefolds consists of 38 components whose general polystable representatives have minimal exponent 1 and form a connected codimension-one adjacency graph with 184 edges and diameter 4.
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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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The GIT Boundary of Quintic Threefolds (Announcement of Results)
The GIT boundary of quintic threefolds consists of 38 components whose general polystable representatives have minimal exponent 1 and form a connected codimension-one adjacency graph with 184 edges and diameter 4.
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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