15 papers
From Finite-Node Conifold Geometry to BPS Structures III: Mediated Triangle Transport and Graded Interaction Data
Abdul Rahman
In previous work, we extracted from a finite-node conifold degeneration the state-data package and then constructed the support-level interaction package en…
From Diaz's Enriques Product to an -Fold Cup-Product Bockstein Family of Integral Hodge Counterexamples
Abdul Rahman
We reinterpret Diaz's construction of Chow-trivial smooth projective varieties violating the integral Hodge conjecture as the level-two case of an \(n\)-fold cup-product Bockstein…
Defect Triangles and Intersection-Space Hodge Atom Shadows for Calabi--Yau Conifolds
Abdul Rahman
We prove a projection-triangle statement for projective Calabi--Yau threefold conifold degenerations and use it to organize an intersection-space Hodge atom shadow package. For a n…
Torsion Trajectories from Local Discriminants to Global Obstructions
Abdul Rahman
For a normal surface singularity, the discrepancy between the ordinary and dual middle-perversity intersection complexes over \(\mathbb Z\) is measured by a finite group \(E\). In…
Integral Perverse Obstructions for Normal Surface Singularities: Resolution Determinants and Monodromy
Abdul Rahman
For a germ of a normal complex analytic surface, let , where and denote the ordinary and dual middl…
Interacting Multi-Node Conifold Light Sectors
Abdul Rahman
We study finite-node conifold degenerations of Calabi--Yau threefolds from the point of view of interacting light sectors. Although each ordinary double point contributes a rank-on…