The logarithmic Picard group and its tropicalization
Tropical Geometry, Amoebas and Polytopes
26 April 14:00 - 15:00
Jonathan Wise - University of Colorado at Boulder
I will describe work in progress with W. Gillam and S. Molcho on the logarithmic Picard group of a family of nodal curves. The logarithmic Picard group is a moduli problem on logarithmic schemes, originally proposed by L. Illusie, and has several features that are impossible to obtain simultaneously within the category of schemes: it is a group, it has a logarithmically etale cover by a logarithmic scheme, it coincides with the usual Picard group when the curve is smooth, and it is complete. The logarithmic Picard group of a curve X also admits a morphism to the Picard group of the tropicalization of X, using which one can recover toroidal compactifications of the Picard group from subdivisions of the tropical Picard group.
University of Bern
Otto von Guericke Universität Magdeburg