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arXiv · 2507.15012

Constructive Degenerations and the Algebraicity of Limiting Hodge

Badre Mounda
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Abstract

We propose a novel constructive framework for approaching the Hodge Conjecture via explicit degenerations. Building on limiting mixed Hodge structures (LMHS), we formulate a criterion under which a rational class of type (p, p) on a smooth projective variety becomes algebraic in the limit of a semi-stable degeneration. We provide examples where vanishing cycles and monodromy explicitly generate new algebraic classes, and propose a general principle: every rational (p, p) class arises as the limit of algebraic cycles under controlled geometric degenerations. This viewpoint opens a new path toward an effective formulation of the Hodge conjecture.

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Badre Mounda. 2025-07-20. Constructive Degenerations and the Algebraicity of Limiting Hodge. https://arxiv.org/abs/2507.15012

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