6 problems

Let $K$ be an algebraically closed complete non-archimedean valued field of characteristic zero. A variety $X$ over $K$ is $K$-analytically Brody hyperbolic if every morphism from…

Let $X$ be a proper variety over $\mathbb{C}$ and let $Y$ be a projective integral variety over $\mathbb{C}$. A pseudo-Brody hyperbolic variety is a variety that is Brody hyperboli…

Let $X$ be a projective integral variety over $\mathbb{C}$. A pseudo-Brody hyperbolic variety is a variety that is Brody hyperbolic outside a proper closed subset. Pseudo-Noguchi c…

Let $k$ be an algebraically closed field of characteristic zero. A variety over $k$ is strongly-pseudo-Brody hyperbolic (respectively, strongly-pseudo-Kobayashi hyperbolic) if ever…

Let $k$ be an algebraically closed field of characteristic zero, and let $X$ be a variety over $k$. A strongly-Brody hyperbolic variety is one for which every model over every subf…

Let $k$ be an algebraically closed field of characteristic zero. A variety $X$ over $k$ is strongly-Brody hyperbolic over $k$ if, for every subfield $k_0\subset k$, every model…