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MiS Preprint

Clutching and gluing in tropical and logarithmic geometry

Alana Huszar, Steffen Marcus and Martin Ulirsch


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.

MSC Codes:
14T05, 20M14, 14A20

Related publications

2019 Repository Open Access
Alana Huszar, Steffen Marcus and Martin Ulirsch

Clutching and gluing in tropical and logarithmic geometry

In: Journal of pure and applied algebra, 223 (2019) 5, pp. 2036-2061