---
_id: '66349'
abstract:
- lang: eng
  text: 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.
author:
- first_name: Dan
  full_name: Abramovich, Dan
  last_name: Abramovich
- first_name: Qile
  full_name: Chen, Qile
  last_name: Chen
- first_name: Steffen
  full_name: Marcus, Steffen
  last_name: Marcus
- first_name: Martin
  full_name: Ulirsch, Martin
  id: '114697'
  last_name: Ulirsch
- first_name: Jonathan
  full_name: Wise, Jonathan
  last_name: Wise
citation:
  ama: Abramovich D, Chen Q, Marcus S, Ulirsch M, Wise J. Skeletons and fans of logarithmic
    structures. <i>arXiv:150304343</i>. Published online 2015.
  apa: Abramovich, D., Chen, Q., Marcus, S., Ulirsch, M., &#38; Wise, J. (2015). Skeletons
    and fans of logarithmic structures. In <i>arXiv:1503.04343</i>.
  bibtex: '@article{Abramovich_Chen_Marcus_Ulirsch_Wise_2015, title={Skeletons and
    fans of logarithmic structures}, journal={arXiv:1503.04343}, author={Abramovich,
    Dan and Chen, Qile and Marcus, Steffen and Ulirsch, Martin and Wise, Jonathan},
    year={2015} }'
  chicago: Abramovich, Dan, Qile Chen, Steffen Marcus, Martin Ulirsch, and Jonathan
    Wise. “Skeletons and Fans of Logarithmic Structures.” <i>ArXiv:1503.04343</i>,
    2015.
  ieee: D. Abramovich, Q. Chen, S. Marcus, M. Ulirsch, and J. Wise, “Skeletons and
    fans of logarithmic structures,” <i>arXiv:1503.04343</i>. 2015.
  mla: Abramovich, Dan, et al. “Skeletons and Fans of Logarithmic Structures.” <i>ArXiv:1503.04343</i>,
    2015.
  short: D. Abramovich, Q. Chen, S. Marcus, M. Ulirsch, J. Wise, ArXiv:1503.04343
    (2015).
date_created: 2026-07-08T07:22:18Z
date_updated: 2026-07-08T07:22:26Z
external_id:
  arxiv:
  - '1503.04343'
language:
- iso: eng
publication: arXiv:1503.04343
status: public
title: Skeletons and fans of logarithmic structures
type: preprint
user_id: '82981'
year: '2015'
...