Séminaire de Géométrie Tropicale
Mercredi 23 octobre, 16h15 salle 1525-502
Gromov compactness in tropical and non-Archimedean geometry
Résumé :
Gromov compactness theorem is a foundational result in
symplectic geometry. It says that the moduli space of stable curves
with a uniform area bound in a closed symplectic manifold is compact.
I will begin by an introduction to this theorem, then I will state and
prove the analogs of Gromov compactness theorem in tropical geometry
and in non-Archimedean analytic geometry. There are three essential
ingredients: Firstly, we need to find the analog of symplectic
structure or Kähler structure; Secondly, we prove a certain
cohomological condition, called the generalized balancing condition;
Finally there is a subtle combinatorial problem, which roughly claims
that the number of vertices of a tropical curve can be bounded by its
tropical area. These results are meant to provide the foundations for
subsequent works on enumerative tropical geometry and enumerative
non-Archimedean analytic geometry.