Rifat Jumagulov

The Hodge conjecture for Fermat fourfolds of odd degree at most 199

Let $X^4_m=\{x_0^m+\dots+x_5^m=0\}\subset\mathbb{P}^5$ be the Fermat fourfold of degree $m$. We give a computer-assisted proof of the Hodge conjecture for $X^4_m$ for every odd $m\le 199$: three geometric closure criteria combined with an exhaustive machine census of the Hodge $(2,2)$-orbits, with a completeness proof...