Constructs semiorthogonal decompositions for derived categories on quasi-smooth derived algebraic stacks indexed by component lattices, with examples for moduli stacks of G-bundles, G-Higgs bundles, and G-local systems.
[↑3, 9, and 17.] [ABKA25] David Alfaya,Indranil Biswas, Pradip Kumar and Anoop Singh
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The work extends non-abelian Hodge theory to transitive Lie algebroids, constructs semiprojective moduli spaces via GIT and Tannakian formalism, and derives a motivic description of their smooth loci in the Grothendieck ring.
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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Semiorthogonal decompositions for stacks
Constructs semiorthogonal decompositions for derived categories on quasi-smooth derived algebraic stacks indexed by component lattices, with examples for moduli stacks of G-bundles, G-Higgs bundles, and G-local systems.
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Lie algebroid Connections, Moduli of $\mathcal{L}$--twisted Principal Objects and motives
The work extends non-abelian Hodge theory to transitive Lie algebroids, constructs semiprojective moduli spaces via GIT and Tannakian formalism, and derives a motivic description of their smooth loci in the Grothendieck ring.
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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