Toroidal b-divisors and applications in differential and arithmetic geometry

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• Ana María Botero, University of Regensburg
• Wednesday 15 March 2023, 14:15-15:15
• CMS MR13.

If you have a question about this talk, please contact Dhruv Ranganathan.

We define toroidal b-divisors on a quasi projective variety over a field. These can be seen as conical functions on a balanced polyhedral space. We show the existence of an intersection pairing for so called nef toroidal b-divisors, which gives rise to a Monge-Ampére type measure on the polyhedral space. We 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 such metrics on line bundles. On the other hand, using a Hilbert-Samuel formula, we compute asymptotic dimension formulae of spaces of automorphic forms on mixed Shimura varieties. Finally, if time permits, we connect our work to the notion of adelic line bundles of Yuan and Zhang, and outline some current research directions.

This talk is part of the Algebraic Geometry Seminar series.

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