article Dan Abramovich author Qile Chen author Steffen Marcus author Martin Ulirsch author 114697 Jonathan Wise author 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. 2015 eng 1503.0434310.1007/978-3-319-30945-3_9 D. Abramovich, Q. Chen, S. Marcus, M. Ulirsch, and J. Wise, “Skeletons and fans of logarithmic structures,” <i>arXiv:1503.04343</i>, 2015, doi: <a href="https://doi.org/10.1007/978-3-319-30945-3_9">10.1007/978-3-319-30945-3_9</a>. Abramovich, D., Chen, Q., Marcus, S., Ulirsch, M., &#38; Wise, J. (2015). Skeletons and fans of logarithmic structures. <i>ArXiv:1503.04343</i>. <a href="https://doi.org/10.1007/978-3-319-30945-3_9">https://doi.org/10.1007/978-3-319-30945-3_9</a> D. Abramovich, Q. Chen, S. Marcus, M. Ulirsch, J. Wise, ArXiv:1503.04343 (2015). Abramovich, Dan, Qile Chen, Steffen Marcus, Martin Ulirsch, and Jonathan Wise. “Skeletons and Fans of Logarithmic Structures.” <i>ArXiv:1503.04343</i>, 2015. <a href="https://doi.org/10.1007/978-3-319-30945-3_9">https://doi.org/10.1007/978-3-319-30945-3_9</a>. Abramovich, Dan, et al. “Skeletons and Fans of Logarithmic Structures.” <i>ArXiv:1503.04343</i>, 2015, doi:<a href="https://doi.org/10.1007/978-3-319-30945-3_9">10.1007/978-3-319-30945-3_9</a>. @article{Abramovich_Chen_Marcus_Ulirsch_Wise_2015, title={Skeletons and fans of logarithmic structures}, DOI={<a href="https://doi.org/10.1007/978-3-319-30945-3_9">10.1007/978-3-319-30945-3_9</a>}, journal={arXiv:1503.04343}, author={Abramovich, Dan and Chen, Qile and Marcus, Steffen and Ulirsch, Martin and Wise, Jonathan}, year={2015} } Abramovich D, Chen Q, Marcus S, Ulirsch M, Wise J. Skeletons and fans of logarithmic structures. <i>arXiv:150304343</i>. Published online 2015. doi:<a href="https://doi.org/10.1007/978-3-319-30945-3_9">10.1007/978-3-319-30945-3_9</a> 663492026-07-08T07:22:18Z2026-07-09T06:15:38Z