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SUMMARY:Ariyan JAVANPEYKAR\, "Finiteness properties of hyperbolic varietie
s"
DTSTART;VALUE=DATE-TIME:20220922T083000Z
DTEND;VALUE=DATE-TIME:20220922T103000Z
DTSTAMP;VALUE=DATE-TIME:20220926T164700Z
UID:indico-event-8165@indico.math.cnrs.fr
DESCRIPTION:I will talk about finiteness properties of hyperbolic varietie
s (some old ones\, some new ones\, and some we expect to be true\, but can
't prove yet). Our starting point is the theorem of de Franchis: given a
variety Y and a hyperbolic Riemann surface C\, the set of non-constant ma
ps from Y to C is finite. The main question I'd like us to ask is simply "
to what extent does this finiteness statement hold for higher-dimensional
hyperbolic targets"? It obviously fails for surfaces (take C x C)\, but it
surprisingly holds for the (orbifold) moduli space of compact hyperbolic
Riemann surfaces of genus g (g>1). I will propose an (in my honest opinion
) reasonable conjecture for *all* hyperbolic varieties. The main result w
ill be a proof of this conjecture for all moduli spaces of polarized vari
eties. Joint work with Steven Lu\, Ruiran Sun\, and Kang Zuo.\n\nhttps://i
ndico.math.cnrs.fr/event/8165/
LOCATION:René Baire (IMB)
URL:https://indico.math.cnrs.fr/event/8165/
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