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SUMMARY:János Kollár (Princeton University)
DTSTART:20200418T160000Z
DTEND:20200418T170000Z
DTSTAMP:20260416T152004Z
UID:Wagon/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Wagon/1/">Wh
 at determines a variety?</a>\nby János Kollár (Princeton University) as 
 part of Western Algebraic Geometry ONline\n\n\nAbstract\nIn this talk we w
 ill discuss topological properties of varieties with many rational points 
 over a function field\, and present joint work-in-progress with Erwan Rous
 seau. More precisely\, we define a smooth projective variety X over the co
 mplex numbers to be geometrically-special if there is a dense set of close
 d points S in X such that\, for every x in S\, there is a pointed curve (C
 \,c) and a sequence of morphisms (C\,c)->(X\,x) which covers C x X\, i.e.\
 , the union of their graphs is Zariski-dense in C x X. Roughly speaking\, 
 a variety is geometrically-special if it satisfies density of "pointed" ra
 tional points over some function field. Inspired by conjectures of Campana
  on special varieties and Lang on hyperbolic varieties\, we prove that eve
 ry linear quotient of the fundamental group pi_1(X) of such a variety is v
 irtually abelian.\n
LOCATION:https://researchseminars.org/talk/Wagon/1/
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