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SUMMARY:Rohini Ramadas (Brown)
DTSTART;VALUE=DATE-TIME:20200515T174500Z
DTEND;VALUE=DATE-TIME:20200515T184500Z
DTSTAMP;VALUE=DATE-TIME:20240910T201817Z
UID:agstanford/7
DESCRIPTION:Title: The locus of post-critically finite maps in the moduli space of self-ma
ps of $\\mathbb{P}^n$\nby Rohini Ramadas (Brown) as part of Stanford a
lgebraic geometry seminar\n\n\nAbstract\nA degree $d>1$ self-map $f$ of $\
\mathbb{P}^n$ is called post critically finite (PCF) if its critical hyper
surface $C_f$ 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)
$. \n\nI will discuss the question: what does the locus of PCF maps look l
ike as a subset of the moduli space of degree $d$ maps on $\\mathbb{P}^n$?
I’ll give a survey of many known results and some conjectures in dimens
ion $1$. I’ll then present a result\, joint with Patrick Ingram and Jose
ph Silverman\, that suggests that in dimensions two or greater\, PCF maps
are comparatively scarce in the moduli space of all self-maps.\n\nThe disc
ussion for Rohini Ramadas’s talk is taking place not in zoom-chat\, but
at https://tinyurl.com/2020-05-15-rr (and will be deleted after 3-7 days)
.\n
LOCATION:https://researchseminars.org/talk/agstanford/7/
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