4 papers
Unlocking the Hodge Conjecture: A Spectral Fingerprint Approach via Gauss-Manin Derivatives
Bita Hajebi, Pooya Hajebi
We present a symbolic analytic framework for addressing the Hodge Conjecture, based on a refined invariant called the Hermitian spectral fingerprint. By projecting out comp…
Spectral Rigidity and Algebraicity: A Unified Framework for the Hodge Conjecture
Bita Hajebi, Pooya Hajebi
This paper presents a novel symbolic analytic framework to address the Hodge Conjecture, utilizing a refined invariant called the Hermitian spectral fingerprint. We modify the fing…
Spectral Fingerprints of Algebraic Cycles: A Hodge-Theoretic Approach to the Hodge Conjecture and Special L-Values
Bita Hajebi, Pooya Hajebi
This paper introduces and develops the "Spectral Fingerprint Philosophy" for detecting algebraic cycles on complex algebraic varieties, particularly K3 surfaces. This framework pro…
Spectral Analysis of Hodge Cycles: A Novel Approach to the Hodge Conjecture via Generalized Moments
Bita Hajebi, Pooya Hajebi
The Hodge Conjecture, posits a profound connection between the topology and algebraic geometry of complex algebraic varieties. It asserts that Hodge cycles, specific elements in th…