4 problems

Growing-cycle conjecture. If $m\equiv \pm 2\pmod{10}$, then $f$ has $5^{t-1}$ growing cycles of length $4$ at every level $\geq t+1$; if $m\equiv \pm 7\pmod{10}$, then $f$ has…

Under the hypotheses of Section 2, let $X$ be the underlying variety, let $\mathcal{F}$ be the given system of rational self-maps, let $X_{\mathcal{F}}(\overline{K})$ denote the po…

Let $I$ be generated by cubic monomials defining a basepoint-free map from $\mathbb{P}^r$ to projective space, and suppose its image is smooth. A map defined by cubic monomials to…

Let $f:X(\Delta)\dashrightarrow X(\Delta)$ be a monomial map associated to a linear map $\phi:N_{\mathbf R}\to N_{\mathbf R}$, where $N$ is a lattice of rank $m$. Let…