Navid Nabijou - 14h00 - Logarithmic structures for toric geometers

Salle Grisvard, IHP, Paris

Salle Grisvard, IHP, Paris


A logarithmic structure on a scheme can be viewed as the data of certain special functions, which we think of as monomials. This point of view underlies the deep interplay between logarithmic and toric geometry, which I will explore in this talk. I will explain how combinatorial techniques from toric geometry generalise to the logarithmic context, with applications to areas including resolutions of singularities and moduli theory. I will explore some of these applications, with a particular focus on the Deligne-Mumford moduli space of stable curves.