Finite-Node Perverse Schobers and Corrected Extensions for Conifold Degenerations
Abstract
We study one-parameter conifold degenerations whose central fiber has finitely many ordinary double points. Working within a deliberately minimal finite-node bulk/localized-sector formalism, we identify the first categorical layer suggested by the corrected finite-node perverse extension and its mixed-Hodge-module package. Assuming that the local ordinary-double-point coupling pattern admits categorical realization in this finite-node setting, we formalize the corresponding local and finite-node data over a chosen bulk category, prove compatibility of their specified shadows with the corrected finite-node perverse extension established in earlier work, and isolate one localized categorical sector per node. We also extract a first finite combinatorial skeleton encoding the nodewise coupling pattern. The paper does not claim a universal perverse-schober theory for arbitrary singular Calabi--Yau degenerations, nor a categorical wall-crossing theory. Rather, it provides the foundational finite-node categorical formalization layer above the corrected perverse and mixed-Hodge-module packages in the conifold degeneration.
Keywords
Cite
@article{arxiv.2604.06597,
title = {Finite-Node Perverse Schobers and Corrected Extensions for Conifold Degenerations},
author = {Abdul Rahman},
journal= {arXiv preprint arXiv:2604.06597},
year = {2026}
}
Comments
Improved scope declarations, tightened boundary conditions, clarified single-node versus finite-node distinction, reduced repetition in Sections 5 and 6. arXiv admin note: substantial text overlap with arXiv:2604.04355