3 problems

Let $X$ be a smooth projective variety, let $K_X$ be nef and effective, and define the irregularity by $q(X)=h^1(\mathcal{O}_X)$. Refined indecomposability conjecture. If…

Let $X$ be a minimal generalized Lagrangian surface of general type. Thus, for a nonzero $w\in\ker\psi_2\subseteq H^0(X,\Omega_X^2)$ of rank $2$, let $V\subset H^0(X,\Omega_X^1)$ b…

Numerical inequality conjecture. If