BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ariyan Javanpeykar (Johannes Gutenberg University of Mainz) DTSTART:20220505T100000Z DTEND:20220505T110000Z DTSTAMP:20260423T035959Z UID:ZAG/208 DESCRIPTION:Title: Sh afarevich's conjecture for canonically polarized varieties revisited\n by Ariyan Javanpeykar (Johannes Gutenberg University of Mainz) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAbstract: Arakelov-Pa rshin proved Shafarevich's conjecture for the (actual) moduli space M_g o f curves of genus g (g>1). Namely\, for every curve C\, the set of isomorp hism classes of non-isotrivial morphisms C \\to M_g is finite. This finite ness result is similar to the theorem of De Franchis: for every hyperbolic curve X\, the set of non-constant morphisms C->X is finite. Interestingly \, M_g is hyperbolic (in any reasonable sense of the word "hyperbolic"). I s maybe the theorem of Arakelov-Parshin and De Franchis an instance of a m ore general finiteness property for hyperbolic varieties/stacks? The answe r is no. The conclusion of the theorem of De Franchis fails for hyperbolic surfaces (such as X x X) and the conclusion of Arakelov-Parshin's theorem fails for the moduli space of canonically polarized surfaces (because it contains copies of X x X). How to remedy this? Guided by finiteness proper ties of compact hyperbolic varieties\, we establish new finiteness propert ies for the moduli space CanPol of canonically polarized varieties by prov ing rigidity properties of pointed maps. Applications include bounds on di mensions of moduli spaces of maps to CanPol. Joint work with Steven Lu\, R uiran Sun\, and Kang Zuo.\n LOCATION:https://researchseminars.org/talk/ZAG/208/ END:VEVENT END:VCALENDAR