4 problems

Let $(X,c6)$ be a non-autonomous algebraic dynamical system, and suppose that some power $(X^n,c6^{\times n})$ has a non-diagonal proper irreducible invariant subvariety. Four-dime…

Linear subvariety conjecture. If $Y$ is $f^{-1}$-invariant or $f^{-1}$-periodic, then $Y$ is a linear subspace of $X$.

Let $X$ be a smooth projective variety over an algebraically closed field $K$ of characteristic $0$, and let $\phi:X\dashrightarrow X$ be a dominant rational self-map. Assume that…

Let $X:=\mathbb{P}^n$, let $f:X\to X$ be an endomorphism with $\deg(f)\geq 2$, and let $Y$ be a closed subvariety of $X$. The linear-subspace conjecture. If $Y$ is $f^{-1}$-invaria…