The logarithmic Picard group and its tropicalization

By S. Molcho, Jonathan Wise. Compositio Mathematica, 2018

50 citations recorded by the source corpus.

We construct the logarithmic and tropical Picard groups of a family of logarithmic curves and realize the latter as the quotient of the former by the algebraic Jacobian. We show that the logarithmic Jacobian is a proper family of logarithmic abelian varieties over the moduli space of Deligne–Mumford stable curves, but does not possess an underlying algebraic stack. However, the logarithmic Picard group does have logarithmic modifications that are representable by logarithmic schemes, all of which are obtained by pullback from subdivisions of the tropical Picard group.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9025a651f4dbbbcf4a7e713d958cc70e67593f2b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Martin Ulirsch
2. Renzo Cavalieri
3. Jonathan Wise
4. Melody Chan
5. Dhruv Ranganathan

In Geometry and Topology

1. Martin Ulirsch
2. Renzo Cavalieri
3. Melody Chan
4. Jonathan Wise
5. Dhruv Ranganathan
6. D. Abramovich

In Statistical and Nonlinear Physics

1. Renzo Cavalieri
2. Jonathan Wise
3. Melody Chan
4. Martin Ulirsch

Citations in the corpus

• A MODULI STACK OF TROPICAL CURVES (2017, methodology): “ neatly characterized over integral bases than non-integral ones [Kat00], with a more manageable deformation theory, and it seems impossible to define a reasonable logarithmic or tropical Picard group [MW18] over a non-integral base. Restricting attention to integral base monoids does not make it imp”