Finite-Node Perverse Schobers and Corrected Extensions for Conifold Degenerations
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908959517966336 |
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| author | Rahman, Abdul |
| author_facet | Rahman, Abdul |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06597 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finite-Node Perverse Schobers and Corrected Extensions for Conifold Degenerations Rahman, Abdul Algebraic Geometry Category Theory 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. |
| title | Finite-Node Perverse Schobers and Corrected Extensions for Conifold Degenerations |
| topic | Algebraic Geometry Category Theory |
| url | https://arxiv.org/abs/2604.06597 |