3 problems

Let $X$ be a smooth complex projective variety and $Y\subset X$ a smooth ample subvariety of codimension $r$. Let $Z$ be a variety and let $\pi\colon Y\to Z$ be a morphism such tha…

Let $X$ be a smooth complex variety and $Y\subset X$ a smooth subvariety of codimension $r$ defined by a regular section of an ample vector bundle on $X$. Let $Z$ be a variety and…

Sommese's extendability conjecture. Any such morphism extends uniquely to a morphism