4 papers
A Deformation Theoretic Reduction of the Hodge Conjecture via Derived Categories and Complete Intersections
Karim Mansour
We propose a geometric and categorical approach to the Hodge Conjecture for all smooth projective complex varieties. By embedding any such variety into a flat family with general f…
A Conditional Reduction of the Rational Hodge Conjecture for Threefolds and Deformation-Theoretic Verifications in Several Families
Karim Mansour
We formulate a concrete geometric approximation hypothesis (Hypothesis~BB) asserting that codimension- Hodge classes on a smooth projective threefold can be realized as speciali…
A Perturbative Multiplicity Theorem for the Borsuk-Ulam Setting
Karim Mansour
We prove a generalization of the classical Borsuk--Ulam Theorem under small perturbations (shaking) of the sphere. We show that for a generic perturbation of a continuous map $f :…
Indecomposable cycles and the case of the twisted Hodge D conjecture
Karim Mansour
We will introduce twisted cycles and their associated regulators to cohomology. We prove the conjecture that this regulator is surjective for a general smooth projective surface. W…