Geometria Logarithmic structures, Artin fans, and the moduli stack of tropical curves
Martin Ulirsch
21-04-2016 - 14:30
AULA 211 (Largo San L. Murialdo,1) Artin fans are logarithmic algebraic stacks that are
logarithmically 'etale over the base field. Despite their seemingly
abstract definition, the geometry of Artin fans can be described
completely in terms of combinatorial objects, so called Kato stacks, a
stack-theoretic generalization of K. Kato’s notion of a fan. In this talk,
following a rapid introduction to logarithmic geometry from a modular
point of view, I am going to give an expository account of the theory of
Artin fans and explain how Thuillier's non-Archimedean skeleton of a
toroidal embedding can be understood as an analytification of the
associated Artin fan. In the special case of a toric variety, this simply
reduces to the fact that the Kajiwara-Payne tropicalization map is a
non-Archimedean analytic stack quotient. Finally, Artin fans also provide
the motivation for a current joint project with R. Cavalieri, M. Chan, and
J. Wise, in which we develop a stack-theoretic framework for the study of
tropical moduli spaces.
org: VIVIANI Filippo
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