Showing math.AGShow all
3 papers · 1 filter
math.AG2025
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…
math.AG2025
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…
math.AG2023
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…