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SUMMARY:Toroidal b-divisors and applications in differential and arithmeti
 c geometry - Ana María Botero\, University of Regensburg
DTSTART:20230315T141500Z
DTEND:20230315T151500Z
UID:TALK194410@talks.cam.ac.uk
CONTACT:Dhruv Ranganathan
DESCRIPTION:We define toroidal b-divisors on a quasi projective variety ov
 er a field. These can be seen as conical functions on a balanced polyhedra
 l space. We show\nthe existence of an intersection pairing for so called n
 ef toroidal b-divisors\, which gives rise\nto a Monge-Ampére type measure
  on the polyhedral space. \nWe then show some applications of this theory.
  On the one hand side\, b-divisors are used to encode singularities of psh
  metrics and we derive Chern-Weil type formulae for\nsuch metrics on line 
 bundles. On the other hand\, using a Hilbert-Samuel formula\, we\ncompute 
 asymptotic dimension formulae of spaces of automorphic forms on mixed Shim
 ura\nvarieties. Finally\, if time permits\, we connect our work to the not
 ion of adelic line bundles of Yuan and Zhang\, and outline some current re
 search directions. \n
LOCATION:CMS MR13
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