Functorial tropicalization of logarithmic schemes: the case of constant coefficients

By Martin Ulirsch. 2013

63 citations recorded by the source corpus.

The purpose of this article is to develop foundational techniques from logarithmic geometry in order to define a functorial tropicalization map for fine and saturated logarithmic schemes in the case of constant coefficients. Our approach crucially uses the theory of fans in the sense of Kato and generalizes Thuillier's retraction map onto the non‐Archimedean skeleton in the toroidal case. For the convenience of the reader many examples as well as an introductory treatment of the theory of Kato fans are included.

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

View Paper: https://www.semanticscholar.org/paper/19586e7c9efa223bba78cdedaad088d0b69eb06b

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. Dhruv Ranganathan
2. Renzo Cavalieri
3. Hannah Markwig
4. Martin Ulirsch
5. G. Mikhalkin

In Geometry and Topology

1. Dhruv Ranganathan
2. Renzo Cavalieri
3. Hannah Markwig
4. Martin Ulirsch
5. G. Mikhalkin

In Statistical and Nonlinear Physics

1. Hannah Markwig
2. Renzo Cavalieri
3. Dhruv Ranganathan
4. G. Mikhalkin

Citations in the corpus

• Tropicalizing the space of admissible covers (2014, background): “The connections between tropical geometry and log geometry are being explored by Gross and Siebert, and Ulirsch, see [21, 36].”