Defines and proves multi-category compatibility of algebraic state data Q_Σ, E_Σ, c_Σ for finite-node conifold degenerations as the first algebraic layer toward BPS structures.
Perverse Extensions and Limiting Mixed Hodge Structures for Conifold Degenerations
7 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Let $pi:X\to\Delta$ be a one-parameter degeneration whose central fiber $X_0$ has a single ordinary double point. The nearby- and vanishing-cycle formalism determines a canonical perverse sheaf on $X_0$, obtained from the variation morphism and fitting into an extension of the intersection complex by a point-supported rank-one contribution. We study this object from the perspective of limiting mixed Hodge theory and Saito's theory of mixed Hodge modules. In the ordinary double point case, we show that the corrected perverse object is the unique minimal Verdier self-dual perverse extension of the shifted constant sheaf across the node, and that its rank-one singular contribution and the corresponding rank-one vanishing contribution in the limiting mixed Hodge structure arise from the same nearby-cycle formalism. We also formulate the analogous structural statements for multi-node degenerations and for more general stratified singular loci. Finally, we explain how Saito's divisor-gluing formalism provides the natural framework for a fuller mixed-Hodge-module refinement of these constructions.
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A global mixed Hodge module P^H is built from local rank-one blocks at each node via Saito gluing; it realizes the corrected perverse object and the finite local vanishing sector.
From a finite-node schober datum the paper constructs the functorial incidence package and quiver assembly, proving it is canonically determined and invariant under equivalences.
Constructs a canonical rigid-flexible decomposition of Hodge atoms for conifold degenerations of Calabi-Yau threefolds, with the total atom fitting an exact sequence controlled by the intersection matrix of vanishing cycles.
Mediated triangle transport yields graded interaction polynomials I_Σ^gr from conifold state data, extending binary support structures for BPS and stability theory.
Defines an interacting multi-node light-sector package for finite-node conifold degenerations of Calabi-Yau threefolds and proves a block-reduced structure theorem that isolates relation collapse and residual global sector interactions.
Cycle relations in multi-node conifold degenerations constrain perverse and mixed-Hodge extensions to an incidence-controlled subspace, yielding R_res = R_sm = R_ext = R_blk in block-separated families.
citing papers explorer
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From Finite-Node Conifold Geometry to BPS Structures I: Algebraic State Data
Defines and proves multi-category compatibility of algebraic state data Q_Σ, E_Σ, c_Σ for finite-node conifold degenerations as the first algebraic layer toward BPS structures.
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Mixed Hodge Modules and Canonical Perverse Extensions for Multi-Node Conifold Degenerations
A global mixed Hodge module P^H is built from local rank-one blocks at each node via Saito gluing; it realizes the corrected perverse object and the finite local vanishing sector.
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From Finite-Node Conifold Geometry to BPS Structures II: Functorial Incidence and Quiver Assembly
From a finite-node schober datum the paper constructs the functorial incidence package and quiver assembly, proving it is canonically determined and invariant under equivalences.
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Hodge Atoms at Conifold Degenerations: F-Bundles, Limiting Mixed Hodge Modules, and the Rigid-Flexible Decomposition
Constructs a canonical rigid-flexible decomposition of Hodge atoms for conifold degenerations of Calabi-Yau threefolds, with the total atom fitting an exact sequence controlled by the intersection matrix of vanishing cycles.
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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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Interacting Multi-Node Conifold Light Sectors
Defines an interacting multi-node light-sector package for finite-node conifold degenerations of Calabi-Yau threefolds and proves a block-reduced structure theorem that isolates relation collapse and residual global sector interactions.
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Cycle Relations and Global Gluing in Multi-Node Conifold Degenerations
Cycle relations in multi-node conifold degenerations constrain perverse and mixed-Hodge extensions to an incidence-controlled subspace, yielding R_res = R_sm = R_ext = R_blk in block-separated families.