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# Tropical and non-Archimedean geometry (2)

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Martin Ulirsch - SFB-Transregio-45-Seminar zur Algebraischen Geometrie

What Seminar Dec 08, 2015 from 02:00 pm to 04:00 pm Bonn, Raum 0.011, Mathematik-Zentrum, Endenicher Allee 60 Sachinidis vCal iCal

Logarithmic structures and the tropical geometry of moduli spaces While $\overline{M}_{0,n}$ admits a well-understood embedding into a toric variety, this is not true for the Deligne-Knudsen-Mumford moduli stacks $\overline{\mathcal{M}}_{g,n}$ of higher genus curves. In this talk I will explain how logarithmic geometry in the sense of K. Kato provides us with a much more general framework for tropicalization that naturally applies to these moduli spaces. The final goal will be a theorem of Abramovich-Caporaso-Payne which gives a modular interpretation for the tropicalization of the algebraic moduli spaces. Given time I will also talk about ongoing work with R. Cavalieri, M. Chan, and J. Wise, where we propose a stack-theoretic generalization of this result.