4 problems

Douglas–Reinbacher–Yau strengthened Bogomolov conjecture. The Chern classes of $E$ satisfy

Let $X$ be a compact complex manifold, and let $(\eta_{d-1},\eta_{d-2})$ be a pair of cohomology classes. A pair is Hodge-Riemann if it satisfies the Hodge-Riemann relations, and i…

Let $X$ be a compact complex manifold of dimension $d$, and let $(\eta_{d-1},\eta_{d-2})$ be a pair of cohomology classes of bidegrees $(d-1,d-1)$ and $(d-2,d-2)$, respectively. A…

Douglas–Reinbacher–Yau conjecture. The Chern classes should satisfy the improved Bogomolov inequality