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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9 Pith papers cite this work, alongside 6,671 external citations. Polarity classification is still indexing.
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UNVERDICTED 9representative citing papers
Classifies rational (quasi-)elliptic surfaces with global vector fields in char p ≠ 2, determining fibers, automorphism schemes, moduli, and Jacobian property except for p=3,5.
K-theory rings of toric and flag varieties are realized as quotients of group algebras from linear families of virtual polytopes, yielding natural relations and descriptions of structure sheaf classes, including in the T-equivariant case.
Constructs an equivalence for torsion coefficients between Zhu's category and Fargues-Scholze's category via Scholze's analytification functor and kimberlite theory, with applications to BunG decompositions and local Shimura varieties.
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.
Proves C^{1,1} regularity for a degenerate fully nonlinear equation on Hermitian manifolds with balanced metrics, yielding unique C^{1,1} solutions to the Donaldson equation.
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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Rational (quasi-)elliptic surfaces with global vector fields in odd characteristic
Classifies rational (quasi-)elliptic surfaces with global vector fields in char p ≠ 2, determining fibers, automorphism schemes, moduli, and Jacobian property except for p=3,5.
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Polyhedral models for K-theory of toric and flag varieties
K-theory rings of toric and flag varieties are realized as quotients of group algebras from linear families of virtual polytopes, yielding natural relations and descriptions of structure sheaf classes, including in the T-equivariant case.
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On the Schematic and Analytic Constructions of the Local Langlands Category
Constructs an equivalence for torsion coefficients between Zhu's category and Fargues-Scholze's category via Scholze's analytification functor and kimberlite theory, with applications to BunG decompositions and local Shimura varieties.
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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.
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Regularity of a Geodesic equation in the space of mixed Volume Forms on Hermitian Manifolds
Proves C^{1,1} regularity for a degenerate fully nonlinear equation on Hermitian manifolds with balanced metrics, yielding unique C^{1,1} solutions to the Donaldson equation.