---
_id: '66334'
abstract:
- lang: eng
  text: The classical clutching and gluing maps between the moduli stacks of stable
    marked algebraic curves are not logarithmic, i.e. they do not induce morphisms
    over the category of logarithmic schemes, since they factor through the boundary.
    Using insight from tropical geometry, we enrich the category of logarithmic schemes
    to include so-called sub-logarithmic morphisms and show that the clutching and
    gluing maps are naturally sub-logarithmic. Building on the recent framework developed
    by Cavalieri, Chan, Wise, and the third author, we further develop a stack-theoretic
    counterpart of these maps in the tropical world and show that the resulting maps
    naturally commute with the process of tropicalization.
author:
- first_name: Alana
  full_name: Huszar, Alana
  last_name: Huszar
- first_name: Steffen
  full_name: Marcus, Steffen
  last_name: Marcus
- first_name: Martin
  full_name: Ulirsch, Martin
  id: '114697'
  last_name: Ulirsch
citation:
  ama: Huszar A, Marcus S, Ulirsch M. Clutching and gluing in tropical and logarithmic
    geometry. <i>arXiv:170607554</i>. Published online 2017.
  apa: Huszar, A., Marcus, S., &#38; Ulirsch, M. (2017). Clutching and gluing in tropical
    and logarithmic geometry. In <i>arXiv:1706.07554</i>.
  bibtex: '@article{Huszar_Marcus_Ulirsch_2017, title={Clutching and gluing in tropical
    and logarithmic geometry}, journal={arXiv:1706.07554}, author={Huszar, Alana and
    Marcus, Steffen and Ulirsch, Martin}, year={2017} }'
  chicago: Huszar, Alana, Steffen Marcus, and Martin Ulirsch. “Clutching and Gluing
    in Tropical and Logarithmic Geometry.” <i>ArXiv:1706.07554</i>, 2017.
  ieee: A. Huszar, S. Marcus, and M. Ulirsch, “Clutching and gluing in tropical and
    logarithmic geometry,” <i>arXiv:1706.07554</i>. 2017.
  mla: Huszar, Alana, et al. “Clutching and Gluing in Tropical and Logarithmic Geometry.”
    <i>ArXiv:1706.07554</i>, 2017.
  short: A. Huszar, S. Marcus, M. Ulirsch, ArXiv:1706.07554 (2017).
date_created: 2026-07-08T07:06:48Z
date_updated: 2026-07-08T07:06:55Z
external_id:
  arxiv:
  - '1706.07554'
language:
- iso: eng
publication: arXiv:1706.07554
status: public
title: Clutching and gluing in tropical and logarithmic geometry
type: preprint
user_id: '82981'
year: '2017'
...