Skeletons and Fans of Logarithmic Structures

By D. Abramovich, Qile Chen, Steffen Marcus, Martin Ulirsch, Jonathan Wise. 2015

56 citations recorded by the source corpus.

We survey a collection of closely related methods for generalizing fans of toric varieties, include skeletons, Kato fans, Artin fans, and polyhedral cone complexes, all of which apply in the wider context of logarithmic geometry. Under appropriate assumptions these structures are equivalent, but their different realizations have provided for surprisingly disparate uses. We highlight several current applications and suggest some future possibilities.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/01672b50c825c4d19b51becdf1a49548eaad5cc9