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Perverse Schobers
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We suggest a possibility for a categorical generalization of the concept of a perverse sheaf, in which vector spaces are replaced by triangulated categories. We call such hypothetical objects perverse Schobers and consider several examples, giving a natural but ad hoc definition in each case. In the simplest case (perverse sheaves on a disk with one possible singular point) we propose, as a categorical analog, the data of a spherical functor.
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Cited by 4 Pith papers
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Sphericalization and the Universal Spherical Adjunction
A construction inverts twists in adjunctions of stable infinity-categories, producing adjoints to the spherical adjunction inclusion and a walking spherical adjunction that classifies them.
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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 fr...
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From Finite-Node Conifold Geometry to BPS Structures III: Mediated Triangle Transport and Graded Interaction Data
Mediated triangle transport yields graded interaction polynomials I_Σ^gr from conifold state data, extending binary support structures for BPS and stability theory.
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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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