The polylogarithm motive over S = P^1 minus {0,1,∞} is realized as the relative cohomology motive of the complement of the hypersurface {1 - z t1⋯tn = 0} in A^n_S relative to the hyperplanes ti=0 and ti=1.
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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
For conifold degenerations, the corrected perverse sheaf on the central fiber is the unique minimal Verdier self-dual extension of the shifted constant sheaf across the node, with its rank-one contributions arising from the same nearby-cycle formalism.
Rigidity is established for isotropic harmonic maps from the 2-torus to CP space arising from complete linear systems, and for broader holomorphic embeddings lacking hyperosculation points when Fubini-Study pullbacks satisfy an extra condition.
Provides the foundational finite-node categorical formalization layer for corrected perverse and mixed-Hodge-module packages in conifold degenerations with finitely many nodes.
citing papers explorer
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A construction of the polylogarithm motive
The polylogarithm motive over S = P^1 minus {0,1,∞} is realized as the relative cohomology motive of the complement of the hypersurface {1 - z t1⋯tn = 0} in A^n_S relative to the hyperplanes ti=0 and ti=1.
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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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Perverse Extensions and Limiting Mixed Hodge Structures for Conifold Degenerations
For conifold degenerations, the corrected perverse sheaf on the central fiber is the unique minimal Verdier self-dual extension of the shifted constant sheaf across the node, with its rank-one contributions arising from the same nearby-cycle formalism.
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Harmonic band theory: rigidity of non-zero degree harmonic maps from 2-torus to complex projective space
Rigidity is established for isotropic harmonic maps from the 2-torus to CP space arising from complete linear systems, and for broader holomorphic embeddings lacking hyperosculation points when Fubini-Study pullbacks satisfy an extra condition.
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Finite-Node Perverse Schobers and Corrected Extensions for Conifold Degenerations
Provides the foundational finite-node categorical formalization layer for corrected perverse and mixed-Hodge-module packages in conifold degenerations with finitely many nodes.