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.
Mixed Hodge Modules and Canonical Perverse Extensions for Multi-Node Conifold Degenerations
6 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We study one-parameter conifold degenerations whose central fiber has finitely many ordinary double points and construct a mixed-Hodge-module refinement of the canonical corrected perverse object associated with the degeneration. We build a rank-one point-supported mixed-Hodge-module block at each node, identify the global singular quotient as $\bigoplus_{k=1}^r i_{k*}\Q^H_{\{p_k\}}(-1)$, and assemble these local blocks via Saito's divisor-case gluing formalism into a global object $\mathcal P^H \in MHM(X_0)$. We prove that $\mathcal P^H$ realizes the corrected perverse object, fits into an exact sequence $0 \to IC^H_{X_0} \to \mathcal P^H \to \bigoplus_{k=1}^r i_{k*}\Q^H_{\{p_k\}}(-1) \to 0$, and that the same quotient realizes the finite local vanishing sector in the nearby-cycle formalism. We further relate the mixed-Hodge-module extension, its realized perverse extension, and the induced extension on hypercohomology carrying the limiting mixed Hodge structure. This gives a theorem-level Hodge-theoretic refinement of the corrected perverse extension in the finite multi-node ordinary double point setting.
fields
math.AG 6years
2026 6verdicts
UNVERDICTED 6representative citing papers
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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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.