Work

The Hodge conjecture for a Delsarte sextic fourfold

Year: 2026

Type: preprint

Abstract: Proof that the Hodge conjecture holds for the sextic fourfold x0^5x3+x3^6+x1^5x4+x4^6+x2^5x5+x5^6=0, conditional on the Hodge conjecture for the degree-30 Fermat fourfold (Shioda/Aoki). Does not resolve the Clay Millennium Hodge problem.v1.2: per-class verification of all 785 Hodge classes (785 pass; 425 explicit plane witnesses, 360 via cited Aoki–Shioda HC for the degree-30 Fermat fourfold plus descent, 0 unresolved); Lean Gröbner certificate. Release: https://github.com/BenFrohman/HODGE/releases/tag/hodge-sextic-v1.2. Conditional on (F); not a solution of the Clay problem.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.23935907

Author: Frohman, Benjamin Stanley

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7225266233

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