Logarithmically Regular Morphisms

Abstract

We consider the stack $\mathcal{L}o{g}_X$ parametrizing log schemes over a log scheme $X$, and weak and strong properties of log morphisms via $\mathcal{L}o{g}_X$, as defined by Olsson. We give a concrete combinatorial presentation of $\mathcal{L}o{g}_X$, and prove a simple criterion of when weak and strong properties of log morphisms coincide. We then apply this result to the study of logarithmic regularity, derive its main properties, and give a chart criterion analogous to Kato's chart criterion of logarithmic smoothness.

19 pages, final version

References in corpus (2)

• A moduli stack of tropical curves
• Toroidal orbifolds, destackification, and Kummer blowings up