Algebraic Geometry Seminar
Rohini Ramadas
Brown University
The locus of post-critically finite maps in the moduli space of self-maps of $\mathbb{P}^n$
Abstract: A degree $d>1$ self-map $f$ of $\mathbb{P}^n$ is called post critically finite (PCF) if its critical hypersurface $C_f$ is pre-periodic for $f$, that is, if there exist integers $r \geq 0$ and $k>0$ such that $f^{r+k}(C_f)$ is contained in $f^{r}(C_f)$.
I will discuss the question: what does the locus of PCF maps look like as a subset of the moduli space of degree $d$ self-maps on $\mathbb{P}^n$? I’ll give a survey of many known results and some conjectures in dimension 1 (i.e. for $n=1$). I’ll then present a result, joint with Joseph H. Silverman and Patrick Ingram, that suggests that in dimensions two or greater, PCF maps are comparatively scarce in the moduli space of all self-maps.
Monday November 2, 2020 at 4:00 PM in Zoom